The Eagles are now guaranteed to be playing Premier League football next season, with a 43-point haul leaving them knocking on the door of the top half.
Andy Carroll was involved in the only incidents of note during a keenly-contested opening 45 minutes between two capital rivals, as he cleared a Kagisho Dikgacoi effort off the line and saw a powerful header of his own beaten away by Julian Speroni at the opposite end of the field.
The England international also had a couple of penalty appeals waved away by referee Martin Atkinson, with Palace skipper Jedinak a touch fortunate to get away with one clear block inside his own area.
It was to be the Australian's lucky day as he was then offered the opportunity to break the deadlock from the spot on 59 minutes, after Cameron Jerome had been tripped by a clumsy challenge from Pablo Armero.
Jedinak made no mistake, drilling high into the top corner to give Adrian no chance, despite the Hammers goalkeeper guessing the right way.
Upton Park rose to its feet for a minute's applause before kick-off in memory of former West Ham forward Dylan Tombides, who died of cancer aged 20 on Friday.
With the match under way, the hosts shaded an uneventful opening 10 minutes in which Carroll enjoyed the best chance, heading over Kevin Nolan's cross after a sloppy clearance from Joe Ledley.
After a tentative opening, Palace gradually settled into the contest and almost broke the deadlock when Dikgacoi headed towards the net, but Carroll was well-placed to clear off the line.
Palace were gathering momentum as Yannick Bolasie turned George McCartney inside-out down the left before delivering a deep cross to Scott Dann, who headed narrowly over under pressure.
The Eagles took the resulting corner quickly and Adrian Mariappa's driven shot was blocked by the diving Nolan, who was fortunate the ball narrowly avoided his arm.
In the 33rd minute, the home side were aggrieved not to be awarded a penalty, and with some justification, as Jedinak appeared to deliberately nudge Carroll over to prevent the forward reaching Matt Jarvis' cross.
West Ham finished the first half the stronger as Mohamed Diame's drilled shot from close range was denied by Speroni and seconds later, the Palace goalkeeper did brilliantly to fend away Carroll's powerful header from six yards out.
The second period began brightly and Carroll should have done better when Stewart Downing's ball reached him at the back post, but the striker hesitated before dragging his shot wide.
Palace could have been given a penalty when Jason Puncheon, who endured a quiet afternoon, was brought down by Armero but referee Martin Atkinson was unmoved.
Only three minutes later, the Hammers left-back was again at fault in the box as he clipped the legs of Jerome.
This time Armero was less fortunate as Atkinson pointed to the spot and Jedinak whipped the ball past Adrian.
Pulis' side could have doubled their advantage in the 67th minute when some frantic defending twice presented Puncheon with chances in the box, but the winger was unable to convert.
Bolasie's cross then just eluded Jerome as Palace began to dictate possession and enjoy the simmering atmosphere at Upton Park.
The home supporters mocked Sam Allardyce when the West Ham boss replaced Jarvis with Carlton Cole in the 70th minute and some jeered Downing when he was brought off for Joe Cole soon after.
Joe Cole's introduction did at least produce some attacking spark for the Hammers as the midfielder first shot wide from the edge of the area before volleying over with four minutes to play, to leave West Ham still seven points clear of the drop zone and looking over their shoulder.