The world number two battled to a 6-7 (4-7) 3-6 7-6 (7-2) 7-5 6-4 victory in a thrilling contest on Rod Laver Arena, where 2021 runner-up Medvedev fended off a match point in the fourth set.
He will now face Stefanos Tsitsipas in what is his second consecutive last-four outing at this tournament after improving his head-to-head record against Auger-Aliassime to 4-0.
Medvedev and Auger-Aliassime met in the semi-finals of last year's US Open, when the former prevailed in straight sets en route to winning the title.
But the Russian, beaten by Novak Djokovic in last year's final, was soon on the back foot in Melbourne, handing Auger-Aliassime a break point at 5-5 when he misjudged a shot that he thought was going out, but dropped in.
Medvedev then compounded that error with a double fault, but Auger-Aliassime fluffed his own lines as he failed to serve out the set before redeeming himself in the tie-break.
Auger-Aliassime continued that momentum in the second set, breaking in a mammoth second game after doggedly staying in a long rally before his opponent pushed a forehand wide.
Facing a two-set deficit, Medvedev battled hard in the third as that too went to a tie-break, which he was leading 2-1 when rain arrived and forced the roof to be closed.
He wasted little time getting the job done once play resumed, Auger-Aliassime finally showing signs of weakness as a couple of unforced errors sealed his fate in a one-sided breaker.
Medvedev survived a match point at 5-4 down in the fourth and reeled off three games in a row as he began to combine power and precision to level matters and tee up a decider.
After fending off three break points in his opening service game, it was Medvedev who broke decisively in game three to claim an advantage that he clung onto in the face of spirited resistance from his Canadian opponent.