Medvedev, the 2019 US Open runner-up, reached his third Grand Slam final by eliminating 12th seed Auger-Aliassime 6-4, 7-5, 6-2.
"I don't think I played my best today but I'm really happy to be in the final," Medvedev said.
Medvedev will play Sunday's final at Arthur Ashe Stadium against the winner of a later semi-final between top-ranked Djokovic and Tokyo Olympic champion Alexander Zverev.
Djokovic is trying to complete the first men's singles calendar-year Grand Slam since Rod Laver in 1969.
The 34-year-old Serbian seeks his fourth career US Open title and his 21st overall Slam crown, which would lift him one above the record 20 he shares with Roger Federer and Rafael Nadal, both absent with injuries.
"We all know what Novak is chasing," Medvedev said. "The only thing I can do is try to play my best."
Medvedev, who lost to Djokovic in this year's Australian Open final, trails Zverev 5-4 in their all-time rivalry and trails Djokovic 5-3.
"If it's (Djokovic), after the Australian Open, I'm going to try to leave my balls on the court to beat him," Medvedev said.
Djokovic would be the oldest US Open finalist since Andre Agassi at 35 in 2005 and could be the oldest US Open champion since Ken Rosewall at 35 in 1970.
By beating Zverev to reach the brink of the Slam, Djokovic would match Federer's all-time record of 31 men's Slam final appearances. Djokovic is 20-10 in major finals.
Zverev defeated Djokovic in a Tokyo Olympic semi-final, rallying from a set and break down to deny the world number one a chance at a "Golden Slam" sweep of major titles and a gold medal.
Djokovic seeks only the fourth men's singles Slam in history after Don Budge in 1938 and Laver in 1962 and 1969.
Australian legend Laver, 83, watched the Open semi-finals from the stands.
With a loss, Djokovic would be the first man with a Slam bid entering the semis not to reach the US Open final.
Djokovic has won 26 consecutive Slam matches, four shy of his all-time record streak from 2015 and 2016 when he won all four major titles in a row.
German 24-year-old fourth seed Zverev, last year's US Open runner-up, is on a career-best 16-match win streak since losing to Auger-Aliassime in the round of 16 at Wimbledon.
Medvedev rescues set two
Medvedev broke at love in the seventh game and claimed the first set after 38 minutes on his sixth of 12 aces.
Auger-Aliassime broke to lead 4-2 in the second set on Medvedev's first double fault but dropped set points in the ninth game on a Medvedev down the line backhand winner and his own netted forehand volley.
Medvedev then broke back on his first chance when the Canadian sent a backhand long.
"I knew I had to do everything at my best because at that point in the match I knew I could break him mentally and that's what happened," Medvedev said.
The Russian broke again at love in the 11th game when Auger-Aliassime netted a forehand and Medvedev held again to seize the second set.
In the third, Medvedev broke for a 2-1 edge on an errant Auger-Aliassime forehand, saved a break point in the fourth game on a service winner and took a 4-1 lead when the Canadian netted a forehand on break point.
Medvedev finished matters with an overhead smash after two hours and four minutes.
Auger-Aliassime, 21 would have been the youngest Slam men's finalist since Juan Martin del Potro won the 2009 US Open at 20 and the youngest to defeat a top-two foe at the Open since Del Potro ended Federer's five-title run in the 2009 final.