The striker scored his 17th and 18th goals of the campaign within the space of nine second-half minutes before Almen Abdi and Matthew Briggs added gloss to the scoreline with further goals in the 66th and 75th minutes.
To add insult to injury for Blackburn, Leon Best was sent off in injury-time for violent conduct.
The win saw Watford close the gap on second-placed Hull, who drew 0-0 with Bristol City on Friday night, to four points, with two games to play.
Hull remain favourites for second place, but Watford's much superior goal difference means the Tigers will need to win at least one of their remaining fixtures to prevent a late charge from the Vicarage Road club, who have now mathematically secured at least a play-off spot.
Blackburn, meanwhile, slipped a place to 20th, just two points clear of the bottom three, after Huddersfield beat Millwall earlier in the day.
After a cagey opening, Watford were denied an opener in the 26th minute by a stunning double save from Grzegorz Sandomierski. Daniel Pudil's cross from the right was headed goalwards by Deeney but the Polish keeper got down well to parry and he reacted superbly to prevent the ball rebounding back into his net after an inadvertent touch from Scott Dann.
Fernando Forestieri also went close in the 38th minute with a curled effort from the edge of the area before Joel Ekstrand headed over from Abdi's corner.
Watford did not have to wait long into the second period for the deadlock to be broken. Seven minutes after the interval Forestieri went past Todd Kane and fed strike-partner Deeney who skipped away from Gael Givet and arrowed a drive across Sandomierski into the bottom corner.
Jordan Rhodes failed to steer his header on target from six yards out in the 60th minute at the other end, and the miss proved costly as Forestieri sent Deeney clear a minute later and the striker clinically slotted in his second of the game and opened the floodgates.
Forestieri created his third goal of the contest with a through-ball for Abdi who fired in his 11th goal of the campaign.
Substitute Briggs got on the act with 15 minutes left as he calmly slotted in from close range after Blackburn had failed to clear Abdi's corner.
The afternoon got worse for Blackburn as Best was sent-off in the last minute of the game for an off-the-ball tussle with Marco Cassetti and will now miss their last three vital games.