Second seed Novak Djokovic will face third seed Roger Federer in the semi-finals of the Paris Masters.
Djokovic fought back from a set down to beat Croat Marin Cilic 4-6 6-2 6-3 in two hours and 12 minutes.
The Serb lost the opening set and went 2-1 down in the third before immediately breaking back and then moving ahead at 5-3.
Australian Open champion Federer beat Japanese 10th seed Kei Nishikori 6-4 6-4 in one hour and 21 minutes.
The Swiss held off a break point late in the first set before immediately moving ahead in the second.
Last week, Federer sealed the Swiss Indoors title for the ninth time and is now one short from 100 tournament wins.
BBC Sport will have live text commentary of the match between Djokovic and Federer on Saturday.
Djokovic showed frustration during his victory, aiming an outburst at his box before serving for the second set, and breaking his racquet after dropping serve in the third.
The 2018 US Open and Wimbledon champion is on a 21-match winning streak and has beaten Cilic in their two most recent meetings.
Djokovic, who has won four Paris Masters titles, will take the world number one ranking from Rafael Nadal on Monday.
Russian world number 18 Karen Khachanov beat fourth seed Alexander Zverev 6-1 6-2 in their quarter-final, setting up a last-four tie with Austrian sixth seed Dominic Thiem.
There were complaints from Zverev over noise coming from Khachanov's box during the match, which finished in just over an hour.
French Open finalist Thiem came from a set down to beat defending champion Jack Sock 4-6 6-4 6-4 in two hours and 16 minutes.