Don Cowie put Watford in front after 19 minutes before City levelled through Nicky Maynard, who was making his first start of the season after undergoing knee surgery in the summer.
Elliot headed the Robins in front midway through the second period before substitute Pitman made sure of the points with an emphatic finish in stoppage-time.
Keith Millen’s side move seven points clear of the relegation zone with the victory, their third in four attempts at Vicarage Road.
Watford are now without a win in seven league games and their new year play-off ambitions must now seem like a distant memory for boss Malky Mackay.
Ross Jenkins came in for Matt Whichelow in the solitary change from the Watford side that drew 1-1 at Reading, while Andy Keogh dropped to the Robins bench to accommodate Maynard and Lewin Nyatanga replaced the injured Jamie McAllister.
The visitors were almost in front after 13 minutes after Maynard broke up play on the left flank to release Martyn Woolford into space. The former Scunthorpe midfielder’s pass found Albert Adomah in the box and his shot flew narrowly wide.
An excellent piece of control allowed Watford’s top-scorer Danny Graham to break clear down the right flank and when David James failed to claim his low cross, Cowie was left with a simple finish to open the scoring.
The goal seemed to rattle City but they were level 13 minutes before the interval in strange circumstances.
A quick thinking – but perhaps subsequently unpopular – Vicarage Road ball boy allowed Nyatanga to take a quick throw as the Watford defence waited for the linesman Warren Atkin’s signal. Referee Craig Pawson allowed play to continue as Woolford enjoyed time to reach the byline and cross for Maynard to tap home.
Watford immediately set about trying to restore their advantage and James did well to hold Graham’s thumping header from Andi Weimann’s right-wing cross.
At the other end a delicate pass from David Clarkson gave Elliot space inside the Watford box but the midfielder dragged his shot across the face of goal.
The game was starting to open up and James held Weimann’s shot at the second attempt after Watford enjoyed further success down the Bristol left.
The Hornets failed to capitalise on an indirect free kick inside the City box after James handled a Woolford backpass, but they had one more clear opportunity before the interval when rookie defender Adam Thompson blazed from eight yards in the 40th minute.
Watford started the brighter of the two sides after the interval and Cowie was narrowly off target with a curling 25-yard free kick in the 55th minute.
An attritional period of play followed but Bristol emerged from it with a 69th minute lead as Elliott was allowed a free header from Maynard’s cross and Watford goalkeeper Scott Loach could only tip the ball into the far corner.
The home side pressed to equalise, but City’s defence stood firm and when Graham did engineer room in the box for Watford’s best chance of the closing stages he sliced harmlessly over.
Pitman definitively settled the issue deep into injury time when Albert Adomah played him down the right channel and he smashed into the roof of the net from a tight angle.