Rune will face Novak Djokovic for the title after the Serbian beat Stefanos Tsitsipas in the other semi-final.
Auger-Aliassime lost on the ATP circuit for the first time since being eliminated in the first round in Astana in early October. Since then, he has dominated three consecutive tournaments in Florence, Antwerp and Basel to qualify for the Tournament of Champions. However, unlike Rune, he did not make his fourth consecutive final appearance. The Danish youngster triumphed in Stockholm in recent weeks and, in addition to Basel, played for the title in Sofia.
See all the stats and details from Rune's win
Djokovic won his eighth straight match against Tsitsipas but needed more than two hours to seal a 6-2 3-6 7-6(4) victory, keeping alive a 13-match unbeaten run as well as his hopes of clinching a seventh title in Paris.
The Serbian made a blistering start to the contest and was almost faultless as he took the opening set in 31 minutes but dropped a set for the first time this week after Tsitsipas rallied superbly in the second to force the decider.
The momentum shifted again in the third set with Djokovic imperious on serve, but he went a mini-break down in the tiebreak before winning the final four points of the match.
"It's very sweet, obviously, when you win matches like this against one of the best players in the world," said Djokovic, who struck 11 aces and won 84% of his first-serve points.
"Deservedly so, both of us went into an even battle all the way until the last point, until the last shot. Some incredible points towards the end. I'm just really glad to overcome this challenge."
