Luca Kjerrumgaard, Edoardo Bove, Mamadou Doumbia and Amin Nabizada were among those to miss opportunities as the Hornets racked up 36 shots, the very last of those finding a breakthrough.
Nobody could deny Watford were worthy winners; they were dominant from the second minute, when Kjerrumgaard scuffed a right-footed effort from close range.
Happy to indulge in a basketball-style game, the Hornets were falling over themselves to break the deadlock, substitute Doumbia heading wide when unmarked and shooting too close to the goalkeeper when through on goal.
Just as Nabizada, Rocco Vata and Edo Kayembe being thwarted late seemed set to send the game to penalties, Bola sent a stunner flying into the roof of the net to book the Hornets' spot in round two.
Alessio Dionisi's side made the early running and could have led inside two minutes when Othmane Maamma's cross was deflected to Luca Kjerrumgaard from close range, but the Dane didn't catch a presentable right-footed opportunity.
From the resulting corner, Iker Bravo fired straight at Vito Mannone in the Crawley goal.
The fast start continued when, after seven minutes, Maamma saw an effort blocked after a short corner, before Bravo's shot was blocked and then Maamma struck powerfully with his left foot and Mannone tipped over.
Inside 10 minutes, there was still time for Maamma to test Mannone again and Bravo did well to pinch possession but took too long to release the pass.
Kjerrumgaard fired well over the bar with his left foot as the Hornets did everything but score in the opening stages.
Just like the friendly against Fiorentina last week, though, Watford went scrappy from there, Kwadwo Baah and Kjerrumgaard guilty of wastefulness in attack.
Crawley gained in confidence and could have led on 25 minutes when Charlie Barker forced debutant Federico Ravaglia into a save, before Klaudio Krasniqi fired over with space around him inside the box.
Stephen Duke-McKenna wanted a penalty as Traore challenged him after he'd got a shot off inside the box, before Kjerrumgaard shot over from a tight angle with his right foot at the other end.
Just after the half-hour mark, Baah raced onto a nicely-weighted Hector Kyprianou pass but was well challenged by Ade Adeyemo before he could shoot, Kyprianou then tamely firing at Mannone.
Kjerrumgaard did find the net with a nice finish on 35 minutes but was flagged offside, before Marc Bola and Omar Traore saw 20-yard efforts blocked as Watford re-established some control.
Mattie Pollock forced a decent save from Mannone with a header, before Kjerrumgaard and Edoardo Bove got in each other's way from 12 yards when attacking the ball in space after a defensive header that had gone straight up in the air.
Profligacy defined the early stages of the second half, too, as substitute Amin Nabizada miscontrolled when put through by Maamma, before Bove and Kjerrumgaard had efforts blocked.
The Italian midfielder was then through himself but denied by a late challenge before Bravo steered a Nabizada cross wide.
After a slower period, the theme resumed on the hour mark as Kjerrumgaard hit the post with a low effort from inside the box, the ball hitting Nabizada on the follow-up and dribbling wide.
Bove tested Mannone again after Maamma had hit the byline and crossed, Bravo the next to have a go but shooting wide from Kjerrumgaard's knockdown.
Maamma was substituted for the returning Rocco Vata after suffering what looked like cramp in his hamstring.
Crawley, roared on by the best part of a thousand visiting fans, sensed their moment and forced Watford's defence into some hurried clearances, but it was the hosts who continued to look most likely.
Mamadou Doumbia came off the bench to head wide, before the Mali forward nearly squared for Martin Payero but underhit it.
Vata spooned an effort over the bar before Vicarage Road screamed for handball when a big Nabizada chance was blocked, but nothing was awarded.
Nine minutes added time prompted another wave of attack, Kayembe seeing an effort deflected into the keeper's arms - but only after Crawley claimed a handball of their own at the other end.
Watford continued to push, Nabizada causing problems down the right, before - incredibly - Doumbia missed another golden chance when put through by Payero, shooting too close to the keeper.
But just as penalties seemed inevitable, a long throw was cleared to Bola, who spanked an effort beyond Mannone and pinched a win Watford deserved but made hard work of.
Watford XI: Ravaglia; Traore, Pollock, Keben, Bola; Bove (Payero 68), Kyprianou, Bravo (Kayembe 68); Baah (Nabizada 46), Kjerrumgaard (Doumbia 68), Maamma (Vata 76)
Unused subs: Bachmann, Clarridge, Zemura, Louza
Nobody could deny Watford were worthy winners; they were dominant from the second minute, when Kjerrumgaard scuffed a right-footed effort from close range.
Happy to indulge in a basketball-style game, the Hornets were falling over themselves to break the deadlock, substitute Doumbia heading wide when unmarked and shooting too close to the goalkeeper when through on goal.
Just as Nabizada, Rocco Vata and Edo Kayembe being thwarted late seemed set to send the game to penalties, Bola sent a stunner flying into the roof of the net to book the Hornets' spot in round two.
Alessio Dionisi's side made the early running and could have led inside two minutes when Othmane Maamma's cross was deflected to Luca Kjerrumgaard from close range, but the Dane didn't catch a presentable right-footed opportunity.
From the resulting corner, Iker Bravo fired straight at Vito Mannone in the Crawley goal.
The fast start continued when, after seven minutes, Maamma saw an effort blocked after a short corner, before Bravo's shot was blocked and then Maamma struck powerfully with his left foot and Mannone tipped over.
Inside 10 minutes, there was still time for Maamma to test Mannone again and Bravo did well to pinch possession but took too long to release the pass.
Kjerrumgaard fired well over the bar with his left foot as the Hornets did everything but score in the opening stages.
Just like the friendly against Fiorentina last week, though, Watford went scrappy from there, Kwadwo Baah and Kjerrumgaard guilty of wastefulness in attack.
Crawley gained in confidence and could have led on 25 minutes when Charlie Barker forced debutant Federico Ravaglia into a save, before Klaudio Krasniqi fired over with space around him inside the box.
Stephen Duke-McKenna wanted a penalty as Traore challenged him after he'd got a shot off inside the box, before Kjerrumgaard shot over from a tight angle with his right foot at the other end.
Just after the half-hour mark, Baah raced onto a nicely-weighted Hector Kyprianou pass but was well challenged by Ade Adeyemo before he could shoot, Kyprianou then tamely firing at Mannone.
Kjerrumgaard did find the net with a nice finish on 35 minutes but was flagged offside, before Marc Bola and Omar Traore saw 20-yard efforts blocked as Watford re-established some control.
Mattie Pollock forced a decent save from Mannone with a header, before Kjerrumgaard and Edoardo Bove got in each other's way from 12 yards when attacking the ball in space after a defensive header that had gone straight up in the air.
Profligacy defined the early stages of the second half, too, as substitute Amin Nabizada miscontrolled when put through by Maamma, before Bove and Kjerrumgaard had efforts blocked.
The Italian midfielder was then through himself but denied by a late challenge before Bravo steered a Nabizada cross wide.
After a slower period, the theme resumed on the hour mark as Kjerrumgaard hit the post with a low effort from inside the box, the ball hitting Nabizada on the follow-up and dribbling wide.
Bove tested Mannone again after Maamma had hit the byline and crossed, Bravo the next to have a go but shooting wide from Kjerrumgaard's knockdown.
Maamma was substituted for the returning Rocco Vata after suffering what looked like cramp in his hamstring.
Crawley, roared on by the best part of a thousand visiting fans, sensed their moment and forced Watford's defence into some hurried clearances, but it was the hosts who continued to look most likely.
Mamadou Doumbia came off the bench to head wide, before the Mali forward nearly squared for Martin Payero but underhit it.
Vata spooned an effort over the bar before Vicarage Road screamed for handball when a big Nabizada chance was blocked, but nothing was awarded.
Nine minutes added time prompted another wave of attack, Kayembe seeing an effort deflected into the keeper's arms - but only after Crawley claimed a handball of their own at the other end.
Watford continued to push, Nabizada causing problems down the right, before - incredibly - Doumbia missed another golden chance when put through by Payero, shooting too close to the keeper.
But just as penalties seemed inevitable, a long throw was cleared to Bola, who spanked an effort beyond Mannone and pinched a win Watford deserved but made hard work of.
Watford XI: Ravaglia; Traore, Pollock, Keben, Bola; Bove (Payero 68), Kyprianou, Bravo (Kayembe 68); Baah (Nabizada 46), Kjerrumgaard (Doumbia 68), Maamma (Vata 76)
Unused subs: Bachmann, Clarridge, Zemura, Louza
