The Posh chief, who was 40 on Friday, toasted his first victory in the London Road hot-seat at the sixth attempt. It was also enough to haul his men off the bottom of the Championship standings.
And Cooper had a familiar face to thank for sealing the points. His first signing, Exodus Geohaghon, headed the crucial goal, his first for the club, 12 minutes from time to break Watford's resistance.
Geohaghon followed Cooper from Kettering Town and was in the right place to beat Scott Loach after George Boyd had clipped a Paul Coutts corner back into the danger area.
It was no more than plucky Posh deserved despite spending much of the second period under the cosh as Watford attempted to end a troubled week on a high after being saved from the clutches of administration late the previous day.
This match only went ahead after a lengthy operation to clear several inches of snow from the London Road playing surface.
That task was only completed moments before kick-off and Watford quickly found themselves frozen out.
Posh hit the ground running with Lee Frecklington needing only nine minutes to break the deadlock after another excellent Boyd assist.
The visitors were left fuming when seeing strong penalty appeals ignored by referee Karl Evans on the half-hour after Danny Graham appeared to have been clattered by Posh keeper Joe Lewis.
Heidar Helguson fluffed a decent headed opportunity late in the opening period and Watford needed until the fourth minute of the second half to haul themselves level when John Eustace coolly slotted past Lewis after a Jon Harley free-kick had taken a kind deflection into his path.
But Geohaghon's priceless header and a stunning late Lewis save to thwart Helguson from point-blank range made sure Posh were wearing the smiles and Watford were reflecting on a fourth defeat in their past five matches.