Dean Shiels gave Rovers a deserved lead five minutes after the break and Gareth Roberts scored for the first time since April to put Rovers 2-0 up.
Heidar Helguson replied with a stoppage-time penalty, but it was too little too late as Watford extended their winless run to six games in all competitions.
The result elevated Doncaster to 12th - five points off sixth - but O'Driscoll insisted he had set no targets for reaching the play-offs.
"I never look at league tables," he said. "Our focus here is on performances. I say this often, but if we get the performances right, the results will follow.
"I'm very happy today because we got the two together.
"We have had a difficult week and it has been nice to finish it off with a performance."
He would go no further when prompted to talk about his Burnley disappointment - which is thought to have arisen because Burnley and Doncaster could not agree a fee on compensation - but he admitted he was flattered by the vocal support he received from the home fans.
"It was nice," he said. "You have good times and bad times at a club and we are doing well at the moment.
"I thought it was a terrific game today. I thought we deserved the win."
For all but the opening exchanges, the win never seemed in doubt.
Having survived a scare in the second minute when Watford's Tom Cleverley miscued, Doncaster had numerous chances to go ahead.
James Coppinger engineered the best in the third minute, driving a low shot across goal that Scott Loach could only parry against the shins of Billy Sharp. The ball ricocheted wide but on a luckier day it easily could have been Sharp's 11th of the season.
A minute later Shiels put a good chance wide, before drawing a good reflex save from Loach, who also did well to tip away a Sharp header as half-time approached.
Shiels eventually scored in the 50th minute, collecting Coppinger's clever back-heeled pass, swivelling in a congested area and rolling a low shot past Loach.
Watford responded well, Henri Lansbury and substitute Will Hoskins bringing good saves from Neil Sullivan.
But Rovers were never seriously threatened and, moments after Shiels drew an excellent stop from Loach, Roberts scored in the 83rd minute with a sweet half-volley from outside the area.
Liam Henderson hit the bar as Watford looked to hit back, before Helguson scored from the spot after Sam Hird brought down Hoskins.
"Their keeper was fantastic," O'Driscoll said. "Big lad, big arms. He did very well for them."
Watford boss Malky Mackay agreed, saying: "He has done very well. There were two or three performances that pleased me and Scott did well.
"But we are disappointed with the performance today.
"I don't think we were as 'at it' as Doncaster. They got to the ball quicker than us when the ball was up for grabs and were just a bit sharper than us. That's disappointing.
"We had a few chances towards the end, but we didn't play as well as we could have done."