Posh's fourth victory in eight games was secured in the 51st minute courtesy of an uncharacteristic error of judgement by England Under-21 keeper Scott Loach and a fine finish from Liam Dickinson.
The Hornets battled to try and get back on terms but on current form they face a real struggle to preserve their Championship status.
This was a fourth successive defeat and, of equal concern for Hornets fans, their team have now gone three games without scoring.
Only a superb double save from Loach prevented the visitors from taking a 12th-minute lead.
Poor communication in the Watford defence allowed Craig Mackail-Smith in on goal and the striker tried to lob the ball over Loach but the keeper saved with his chest.
The ball then fell to Dickinson and the keeper parried away the striker's powerful shot from a tight angle.
The Hornets had another close shave shortly before the break but this time they had the post to thank when Aaron McLean turned sharply on the edge of the area and fired a half-volley against a post.
But Watford, and their keeper in particular, were the architects of their own downfall six minutes after the break.
Loach bizarrely came right to the edge of his area to challenge for a ball, lost out in a 50-50 challenge and then could only watch Dickinson's superb 25-yard lob sail over him as he back-tracked towards his own line.
Defender Adrian Mariappa twice went close as the Hornets tried to salvage something from the remainder of the contest.
Tom Cleverley struck a 20-yard free-kick narrowly over, while Will Hoskins' ambitious 35-yard effort also just cleared the bar, but Watford were unable to stop themselves from sliding to a third straight home defeat.