Rafael Nadal stayed on course to finish the year as number one after he saw off Jo-Wilfried Tsonga 7-6 (7-4) 6-1 to reach the Paris Masters semi-finals.
The Spanish 19-time Grand Slam singles winner, who now faces Denis Shapovalov, needs to win the event to guarantee top spot heading into 2020.
Earlier, number one seed Novak Djokovic thrashed Stefanos Tsitsipas 6-1 6-2.
He will face Grigor Dimitrov on Saturday after the Bulgarian defeated Chile’s Cristian Garin 6-2 7-5.
Djokovic, winner of 16 Grand Slams, took only 58 minutes to overcome the Greek player.
The Serb, who will lose his number one ranking to Nadal next week, said: “I played one of the best matches of the season.
“I lost to Stefanos about three weeks ago in Shanghai. And obviously I went through the videos and understanding on what I did well, what I didn’t do so well, what I can do better.”
In Friday’s other quarter-final, Canada’s world number 28 Shapovalov ended Frenchman Gael Monfils’ hopes of playing at the ATP Finals with a 6-2 6-2 win in just under an hour.
Italian Matteo Berrettini, who reached the US Open semi-finals, takes the last berth in the final event of the season, which begins on 10 November in London.