In his first 90-minute stint since damaging a hamstring against Manchester City a month ago, Postiga scored our equaliser and won the penalty that Jamie Redknapp drilled home for the winner in the second half.
The Portuguese striker looked lively throughout and some of his runs bamboozled the home defence but he had to settle for one goal against a Dons side that would have run all night.
Other highlights included club captain Redknapp completing his second full as he builds up his fitness after injury and another Jamie, this time O'Hara - 13 years Redknapp's junior - impressing in central midfield after coming on as a substitute at the start of the second half.
Wimbledon started brightly and took the lead after 19 minutes as Gary Smith dribbled from right to left across the 18-yard line before hitting a low shot back across Rob Burch and into the right corner.
Rohan Ricketts went close twice and home keeper David Martin was out quickly to block at Postiga's feet from Stephen Kelly's clever pass.
A response looked inevitable and arrived after 34 minutes. Mark Hughes played the ball in to Mark Yeates, the home side failed to deal with it and it sat up perfectly for Postiga to crack into the top corner from 18 yards.
The Dons might have gone ahead just before the break when Morgan's cross just needed a finishing touch from close range but it was one-way traffic - barring one magnificent save from Burch - in the second half.
Martin twice pushed away snapshots from the lively Yeates in the box and Ricketts somehow failed to convert Dean Marney's deep cross.
Again, a Spurs goal looked on the cards and this time arrived via the penalty spot after 58 minutes.
There were few arguments as Dons defender Harry Ntimbah-Zeh tugged harder and harder at Postiga's shirt as they went for Ricketts' fine cross - it couldn't have been more blatant if he'd have taken it off. The referee duly pointed to the spot and Redknapp made no mistake from 12 yards.
To their credit, Dons rallied and forced the save of the match from Burch, arching backwards to tip over Cornwall's point-blank header after 68 minutes.
Ricketts tried his luck again late on and O'Hara almost scored the goal his second half performance deserved, his well-struck drive gathered by Martin.
The only note of concern came minutes from time when Burch was replaced by Nicky Eyre having landed awkwardly and turned his ankle.
19mins: GOAL. Smith dribbled from right to left across 18-yard line, hit low shot back across Burch into bottom right corner. 0-1.
34mins: GOAL. Hughes injected pace into move, Yeates tackled on edge of the box but loose ball dispatched into top corner by Postiga. 1-1.
58mins: GOAL. Ntimbah-Zeh almost ripped shirt off Postiga from Ricketts cross, penalty awarded, Redknapp drilled home spot kick. 2-1.
Line-ups: Wimbledon: Martin, Deacons, Puncheon, Wolleaston, Ntimbah-Zeh, Oyedele, Goma, Smith, Morgan (Gordon, 73), Cornwall, Dove (Jarrett, 44). Subs: McKoy, Mouter, Slater.
Spurs: Burch (Eyre, 88), Kelly, McKie, Hughes (O'Hara, 45), Mabizela, Bunjevcevic, Marney, Redknapp, Yeates (Barnard, 83), Postiga, Ricketts. Subs: Ifil, Lee.
Helder Postiga was the star turn as our reserves overcame a spirited Wimbledon outfit 2-1 at Milton Keynes on Wednesday night.