The Russian was briefly in trouble in the second set, when Auger-Aliassime could not serve it out after establishing a 5-2 lead, but he was otherwise in charge as he nailed a 6-4 7-5 6-2 semi-final win.
It means the man beaten by Rafael Nadal in a mesmerising 2019 Flushing Meadows final will be back on Monday (AEST) to go after a first Major title.
World No.2 Medvedev looked in good shape, and it was always going to take a major effort for No.12 seed Canadian Auger-Aliassime to test him.
That test arrived when Auger-Aliassime led by a break in the second set but could not finish the job.
Medvedev soon levelled the set at 5-5 and Auger-Aliassime coughed up an ugly double fault to give him a look at 0-30 in the next game, before fluffing a volley to present the Russian with three game points.
A forehand into the net moved Medvedev into a 6-5 lead, serving for a two-set cushion, and a fuss-free game moved the Moscow-born 25-year-old one step away from the final.
Auger-Aliassime was looking to follow his fellow Canadian Leylah Fernandez into a US Open final this weekend, yet the failure to seize that one big chance was his undoing.
Playing ahead of the second semi-final between Grand Slam-hunting Novak Djokovic and Olympic champion Alexander Zverev, it was plain sailing in the third set for Medvedev.
He struck a startling forehand winner around the net post late in the contest, demonstrating the sort of class to test the best.
Medvedev described the clash as "a strange match", saying in an on-court interview: "I think everybody thought it was going to be one set all, and you never know where the match is going to go.
"I managed to save the set points: he missed one volley and I won one good point, and the match turned around completely. I don't think I played my best today, but I'm really happy to be in the final."
He quite reasonably described his five-set thriller against Nadal two years ago as "a crazy match".
"If it's going to be a crazy match on Sunday, I just hope I can win this time," he added.