Auger-Aliassime was chasing his first Masters title and looked set for victory before a resurgent Rublev, 26, who had been struggling with a fever during the tournament, recovered to prevail in a little under three hours.
The Russian had come into the tournament in Madrid in poor form having lost his previous four matches on the tour but dropped only two sets en route to the title.
"No words, if you knew what I've been through in the last nine days, you wouldn't imagine that I would be able to win a title. Last six weeks I was losing in the first rounds," Rublev said.
"I was (close to pulling out) because there were few issues I couldn't fix, but I have to give full credit to the doctors. They were magical and did some tricky things. Somehow I was able to play. I've never seen this in my life.
"I would say this is the most proud title of my career. I didn't sleep well the last three-four days."
Auger-Aliassime had moved into the final when three of his five opponents in Madrid gave him walkovers, including top seed Jannik Sinner, who pulled out with an injury before their quarter-final clash.
Questions about whether the unseeded Canadian deserved to be in the final were put to rest in the opening set when he clinically dismantled Rublev's serve.
Rublev had the worst possible start when he was broken to love in the first game of the match with two double faults and the Russian quickly found himself 4-1 down as Auger-Aliassime fired several winners.
The seventh seed fought back and managed to break Auger-Aliassime but the Canadian was well in control by then, serving well to make optimal use of his strong forehand before sealing the opening set on serve with a resounding winner at the net.
But Rublev, who had eliminated second seed and home favourite Carlos Alcaraz in the quarter-finals, was far more aggressive with his shot-making in the second set which went with serve.
The Russian also found his range on his first serve and constantly put Auger-Aliassime on the backfoot before clinching the decisive break when he was up 6-5 to force a decider.
It was a case of deja vu in the final set too which went with serve until Rublev broke again at 6-5.
Auger-Aliassime was under pressure as he served to stay in the contest but he made two double faults, the second handing the title to Rublev in an anti-climactic end to the final.
5°C