Morison was sporting a hefty bandage following a nasty clash of heads in Saturday's goalless first leg, but Millwall's summer signing from Stevenage left the Terriers' defence with a headache as he hit his 23rd goal of a stunning debut season.
And home skipper Robinson ensured there would be no late comeback from a disappointing Town side with a late header.
The Lions will face Swindon a week on Saturday as they attempt to bury their play-off hoodoo - they have missed out on promotion in their previous five attempts.
Kenny Jackett's side lost out to Scunthorpe in the final last year, but with Morison in red-hot form they will be confident of going one better this term.
Backed by a raucous crowd, they went at Huddersfield from the off and Robinson glanced a Neil Harris cross wide before Morison's header was saved by Alex Smithies.
The Town keeper then had to dive full-stretch to claw away a deflected 20-yard drive from Jimmy Abdou.
But Huddersfield had only themselves to blame when Millwall took the lead in the 23rd minute.
Left-back Robbie Williams misjudged Tony Craig's high ball allowing Danny Schofield to race to the byline and his low cross was palmed by Smithies straight to the feet of Morison, who made no mistake from six yards.
The hosts should have been two up five minutes later when Morison this time wandered into space down Huddersfield's left, but defender Jack Smith blasted his cut-back narrowly wide.
Morison also headed Scott Barron's corner over the top as a one-sided first half came to a close.
Barron came agonisingly close to doubling Millwall's advantage midway through the second half when his angled drive crashed back off the angle of post and crossbar.
But despite Millwall only holding a narrow lead, Huddersfield never looked like getting back into the game with their 23-goal striker Jordan Rhodes hardly having a kick.
Instead Lee Novak had the best of their all too rare chances, firing straight at Lions keeper David Forde in the first half and blazing over the crossbar in the second.
But the Lions were not unduly troubled and they secured a second successive appearance in the final with eight minutes remaining.
Barron swung in another dangerous corner and Robinson rose highest to power his header past Smithies and spark another knees-up in south London.