The Terriers, leading 2-0 from the first leg, went ahead on the night through leading scorer Jordan Rhodes, only for Daniel Powell to level before half-time.
Although substitute Alan Smith scored with a header in injury-time, Huddersfield held on to make sure of their place at Wembley.
Rhodes, English football’s leading goalscorer this season, fired Simon Grayson’s side into a 1-0 second leg lead in the 18th minute to give Huddersfield what proved to be an unassailable three-goal cushion.
Powell had given the Dons hope with a 39th-minute equaliser, but goals from Rhodes and Jack Hunt in the first leg last Saturday had set Town on their way and they just held on.
In their record-breaking eighth play-off appearance Town endured some anxious moments before securing a deserved second successive play-off final.
It could have gone horribly wrong for the home side though had Dons striker Charlie MacDonald converted two golden chances either side of the interval.
But Town weathered the storm to condemn Karl Robinson’s men to more play-off misery after they slipped out at the same stage last season.
Lee Novak spurned an early chance to settle any Huddersfield nerves when he pulled his shot from inside the penalty area just wide.
But the home side secured the game’s all-important first goal in the 18th minute.
Hunt arced a deep free-kick into the visitors’ area and Rhodes pounced on to Danny Ward’s flick-on, his first touch allowing him time to steer the ball low into Dons goalkeeper David Martin’s left-hand corner.
The West Yorkshire club’s three-goal cushion prompted wild celebrations among the home faithful, including Town owner Dean Hoyle in the stands.
But the Dons served warning that there was still a long way to go when Dean Bowditch’s goalbound curler from the edge of the area was deflected over the crossbar by Huddersfield skipper Peter Clarke.
Town goalkeeper Ian Bennett was forced off with what appeared to be a hand injury 12 minutes before the break and was replaced by Alex Smithies.
Smithies’ first touch was to pick the ball out of the net six minutes later.
Dons striker Powell spun on a sixpence on the edge of the area when collecting Adam Chicksen’s pass and lashed a fierce shot inside Smithies’ far post.
The home side were then given a real let-off in the 43rd minute. Powell’s bouncing cross was headed inches wide by the sprawling MacDonald amid furious protests from the visitors that Clarke had bowled him over just before half-time.
Most in the Galpharm Stadium held their breath when MacDonald’s toe-poke rolled inches wide following Darren Potter’s slide-rule pass three minutes into the second half.
But Town regained some composure and Dons keeper Martin kept his side in the tie just before the hour, saving brilliantly twice in quick succession to keep out Hunt’s drive and then Novak’s stinging follow-up moments later.
Smithies pulled off two superb saves to deny Dons substitute Jabo Ibehre and Powell in the closing stages and Smith then dived in to head home at the back post in the second minute of time added on, but it was not enough to save the visitors.