The striker, who is on loan with Posh from League One Brighton, netted with a stunning long-range lob in the second half to sink Watford.
His second Peterborough goal secured back-to-back wins for Jim Gannon's side for the first time this term and offered a glimmer of hope that they might yet beat the drop.
Defeat also dragged the Hornets closer to the relegation mire, with Malky Mackay's men having lost their last four matches.
The Hornets could have no complaints and only woke up after Dickinson had found the net.
Their England Under-21 goalkeeper Scott Loach kept them on level terms early on with a fine double save from Craig Mackail-Smith's fierce shot and Dickinson's follow-up.
Don Cowie wasted Watford's first opportunity when he shot wide before Henri Lansbury met a cross from Martin Taylor but blazed his effort over the top.
But the Hornets failed to trouble Posh keeper Joe Lewis during the first half, and with the frustration growing around Vicarage Road Arsenal loanee Lansbury picked up a needless booking for kicking the ball away.
As half-time approached Craig Morgan headed Tommy Rowe's cross over the crossbar, and the hosts had another let-off when Aaron Mclean's 20-yard drive came back off the post.
The visitors came close to opening the scoring just after the break when McLean let fly with a shot which fizzed inches wide with Loach struggling to get across his goal.
Posh still looked the most likely side to break the deadlock - and they eventually took a deserved lead in the 51st minute.
Loach was forced to come charging out of his goal to clear ahead of Mark Little but the ball fell to Dickinson, who calmly side-footed it back over the stranded goalkeeper and into the net from all of 35 yards.
Shell-shocked Watford finally tested Lewis when Adrian Mariappa's deflected shot was clawed away by the visiting keeper.
Home striker Danny Graham then fluffed his lines in front of goal from Tom Cleverley's cross when he got underneath the ball and ballooned a shot over the top.
Posh could have had a second when Martin Taylor headed against his own crossbar, while Hornets substitute Will Hoskins came agonisingly close to equalising at the death with a long-range shot which flew just over the bar.