John Eustace and Carl Dickinson were the Watford players denied and, although Scott McGleish shot wide for Rovers, they won the shootout 4-2 with the final kick not taken at the Memorial Stadium on Tuesday night.
Both of the goals in 120 minutes of highly competitive cup-tie action came in the opening five minutes.
Marvin Sordell slid in to convert a low cross from Craig Forsyth just two minutes in and three minutes later Matt Harrold equalised with a superbly-struck shot on the turn from 25 yards.
Both sides had chances to win before the shootout which was completed by the coolest of spot-kicks from Rovers' substitute Mustapha Carayol.
Jo Kuffour, Adam Virgo, and Wayne Brown also scored for Rovers in the shootout, while Sordell and Adrian Mariappa netted for Watford.
The Championship side had the better scoring opportunities in normal play and striker Troy Deeney could have had a first-half hat-trick. He should have scored on 20 minutes when put through by Sordell, but Bevan came to Rovers' rescue with what was the first of several crucial saves.
Deeney was denied twice more by Bevan before the break and the Rovers goalkeeper was undeniably the man of the match.
Both sides hit the woodwork, Watford twice through shots from David Mirfin and Eustace, while Kuffour saw a first-half effort deflected up onto the crossbar.
League Two Rovers made up for any deficiency in class with a whole-hearted effort and contributed fully to an absorbing cup battle.
Watford boss Sean Dyche will feel his side should have won on the balance of play, but Rovers stuck solidly to their task and when their defence was breached the giant Bevan repeatedly came to the rescue.
Paul Buckle's team will now visit Leyton Orient next week.