Craig Mackail-Smith signed off from London Road in style as his 34th goal of the season booked Posh a showdown with the Terriers at Old Trafford on Sunday, May 29.
The Scotland international will leave for bigger things in the summer but could help Posh to promotion first after his close-range effort sealed victory over the Dons.
Karl Robinson's side held a 3-2 lead from the first leg which was wiped out early on by Peterborough captain Grant McCann's free-kick.
And Mackail-Smith then struck in his final home appearance for the club to put Darren Ferguson 90 minutes away from his third promotion as Posh boss.
Mackail-Smith struck early during Sunday's first leg and had an early chance again when Tommy Rowe found him inside the area but his low shot was turned around the post by goalkeeper David Martin as the hosts started strongly.
And they wiped out the deficit in their next attack with their 109th league goal of the season when McCann struck in the 11th minute.
Lee Tomlin was clipped to the right of the area and McCann stepped up to bend a free-kick over the wall and in at the foot of Martin's near post.
The goalkeeper should have done better but the Dons recovered quickly and Angelo Balanta soon had Paul Jones scrambling to make a save at the other end.
Jones was in the Posh side as first-choice Joe Lewis fractured a kneecap during the first game and made some strong claims from a string of corners as Dons had a spell of pressure.
But it was Ferguson's men who came close to going ahead on aggregate when Grant Basey burst into the area and drove a ball across the six-yard line which narrowly evaded Mackail-Smith and James Wesolowski at the back post.
The ever dangerous Mackail-Smith forced Martin into another save at his near post before the visitors should have equalised before the break.
A cross from the left found its way through to Daniel Powell and he smashed a volley past Jones which shook the bar before bouncing clear.
Mackail-Smith had barely touched the ball in the second period before he bundled in a second in the 54th minute.
Tomlin chipped a cross in from the right which Dons centre-halves Gary MacKenzie and Sean O'Hanlon made a mess of clearing.
The ball fell for George Boyd and, although Martin did well to keep out his shot, Mackail-Smith was on hand to smuggle
the ball in from close range at the second attempt.
The visitors immediately broke into the area and had claims for a penalty waved away when the ball appeared to strike Mark Little.
Tomlin then thrashed the ball in from a tight angle but referee Colin Webster had already blown for a foul on Boyd.
Tommy Rowe was next to be denied when his low shot was cleared by MacKenzie as Posh looked for the goal which would have sealed victory.
Martin had to be alert to palm a header over from his own skipper Dean Lewington as the clock wore down before Mackail-Smith hit the post after charging through a tired backline.
It was a poor finish but Ferguson's men completed the victory to set up an Old Trafford final with Lee Clark's Terriers next Sunday.