Karl Robinson's side dominated large swathes of the second leg at the Galpharm Stadium after losing the first leg 2-0 at home on Saturday, but Huddersfield did just enough to eke out the win.
Scotland forward Jordan Rhodes slipped home his 40th goal of the season to ease the home fans' nerves, but MK Dons came roaring back brilliantly with Daniel Powell finishing from the edge of the box to equalise on 39 minutes.
MK continued to carry the game to the home side in the second period and won the game deep into injury time when substitute Alan Smith headed home from close range a couple of minutes into the four added on.
It was too little, too late for the visiting side who fall short again in their ambition to reach the play-off final. They have yet to go beyond the last four in four attempts. Huddersfield return to Wembley a year after losing to Peterborough.
Simon Grayson's team will face Yorkshire neighbours Sheffield United in the final on May 26 after United eked out a 1-0 win over Stevenage in the other semi-final on Tuesday night.
MK Dons carried the fight to the home side for most of the evening as they enjoyed over 60 per cent of possession. Home goalkeeper Ian Bennett was forced into action early on to thwart Charlie MacDonald before he was carted off injured with a wrist injury to be replaced by Alex Smithies on 32 minutes.
With the scores locked at 1-1 heading for the break, MK Dons should have been awarded a penalty when MacDonald was bundled over by Sean Morrison but the referee said no.
MacDonald blew a golden chance to give his side the lead minutes after the break when he knocked a shot wide under pressure from Smithies with David Martin producing solid stops from Hunt and Lee Novak at the other end as the home side hit on the break.
Huddersfield were denied their own penalty when Dean Lewington clearly barged Peter Clarke to the ground before Smithies was called into action in the dying seconds to make fine stops from Jabo Ibehre and Powell.
Smith had the final say late on, before the former Leeds United player was mobbed and apparently attacked by celebrating home fans at the full-time whistle on his return to West Yorkshire.