Jedinak almost sealed the victory single-handedly after playing most of the game with a back knock to his leg, yet in the dying moments of normal time launched himself at a cross that almost beat the keeper.
But it was former Sunderland striker Kevin Phillips who proved to be the hero at Wembley for Palace, as he netted a penalty in the first half of extra time to secure promotion for the London club in a tight affair.
Wilfried Zaha, playing his final game for the club before a move to Manchester United, won the spot-kick, tempting Marco Cassetti into a clumsy lunge in the area with a trademark tricky run.
And, though Fernando Forestieri came within inches of forcing a penalty shootout, Palace held out to ensure they would return to the English top flight.
Ian Holloway named an unchanged line-up for the Wembley showpiece, sticking with the same team which had beaten Brighton 2-0 in the second leg of the semi-final.
Gianfranco Zola, by contrast, made two changes from the side which earned a dramatic late win over Leicester, with Daniel Pudil coming in for Matthew Briggs and Jonathan Hogg replacing Cristian Battocchio.
Both teams struggled to create anything of note in the early stages, with Kagisho Dikgacoi's early injury - which meant the midfielder had to be replaced by Stuart O'Keefe after 16 minutes - the only real incident of the opening stages.
Zaha and Matej Vydra both tried to inject life into the contest for their respective teams, but a blocked shot from the latter after 32 minutes proved the best opportunity of a dour half which was brought to a close with the teams level at 0-0.
Watford started the second half the brighter of the two sides, but it was Palace who finally managed to create the game's first genuine opening, striker Aaron Wilbraham bursting through on the counter-attack only to see his tame shot well saved by former Arsenal player Manuel Almunia.
That chance gave Holloway's men a boost and Almunia was once again forced to come to Watford's rescue to deny O'Keefe after he had latched on to Zaha's pull-back following a wonderful ball over the top from Mile Jedinak.
The Spaniard then sprung into action again from the resulting corner, denying Wilbraham once more from close range.
Veteran Phillips was thrown into the fray a minute later, but it was former Norwich striker Wilbraham who continued to be the man at the centre of Palace's forays forward. And he was prevented from scoring yet again as the Watford shot-stopper made another fine save from point-blank distance.
But Holloway's charges could not force their way through, and were left to settle for extra time.
Watford gained confidence after seeing out a difficult second-half spell and came close to snatching a surprise advantage when Julian Speroni somehow kept out Troy Deeney's effort from two yards after the forward had collected Almen Abdi's low cross.
However, in the end it would be Zaha who made the telling impact, as he was felled by Cassetti just inside the area after a surging run, enabling Phillips to step up and power the resulting spot-kick into the top corner.
Palace survived a scare at the death thanks to Joel Ward, who cleared Forestieri's late effort of the line, but were good value for their lucrative victory at Wembley.