After Charlie Taylor had stunned Molineux by giving Leeds an 11th minute lead, Nouha Dicko and Benik Afobe took charge to put Wolves on course for what looked to be a routine fourth successive victory.
Dicko grabbed a first-half double to take his tally for the season to 13 before Afobe grabbed his 29th goal of the season - 19 of them on-loan for MK Dons before he made a £2million January switch to Wolves from Arsenal - at the start of the second half.
But a 65th minute own goal from Wolves captain Danny Batth gave Wolves the jitters and Alex Mowatt cashed in on their nerves to fire Leeds level before substitute Edwards pounced two minutes from time.
Leeds had been unbeaten in their previous three away games and had only lost on the road twice in 2015.
But Wolves ultimately had too much fire-power for them to complete a miserable Easter for Leeds head coach Neil Redfearn, whose future at Elland Road remains shrouded in doubt.
Redfearn had seen his assistant Steve Thompson suspended last week, with United then crashing to a 3-0 defeat at home to Blackburn on Good Friday.
In a lively opening, Dicko had twice threatened to give Wolves the lead in the opening 10 minutes when he flashed a shot wide and saw a close-range header fly over the bar before Taylor stunned Wolves following a dreadful piece of play by Kevin McDonald.
McDonald was in possession but was forced back to his own goalline by Leeds’ debutant Kalvin Phillips.
Rather than attempt to clear up field, McDonald tried to play the ball across the face of his own area. His clearance bounced off the Wolves central defender Richard Stearman and fell kindly into the path of Taylor, who had the simple task of side-footing his finish under goalkeeper Carl Ikeme.
Fortunately for McDonald his blushes were quickly spared by the lively Dicko in the 19th minute.
Bakary Sako did have a golden chance to equalise only to shoot weakly at goalkeeper Marco Silvestri but Wolves only had to wait another three minutes to draw level.
Afobe made a powerful run down the right wing and his cross flew to the far post, where Dicko beat the despairing lunge of Scott Wootton to calmly stab the ball home.
Wolves should then really have turned their dominance into a lead, only for Silvestri to palm away James Henry’s powerful drive following Dominic Iorfa’s cross.
The busy Silvestri denied Henry again at his near post four minutes before half-time, with Sako then seeing his powerful drive deflected over the bar by Sol Bamba.
But there was nothing Silvestri could do when Sako turned provider for Dicko as the first half moved into stoppage time. Dicko timed his run to perfection to stay onside and his angled cross-shot whistled past the right hand of the Italian keeper.
Former Wigan marksman Dicko also then had an unwitting hand in Afobe’s 48th minute strike. Batth saw his shot bounce off Dicko and fall kindly into the path of Afobe, who reacted smartly to make no mistake from close range.
Unfortunately for Batth his next intervention was rather more costly when he sliced Mowatt’s hopeful cross into his own net just as Ikeme came out to collect the ball.
That slip by their skipper unnerved Wolves and Mowatt was on hand to take full advantage.
Wolves failed to clear the ball and, as the space in front of him opened up, Mowatt let rip from 25 yards and saw his 74th minute drive fly past Ikeme.
It looked good enough to earn Leeds a hard-earned point only for Edwards to flash home a header from McDonald’s left wing cross two minutes from time.