Garbine Muguruza saved three match points before beating Anastasija Sevastova to reach the WTA Elite Trophy semi-finals in Zhuhai, China.
The Spaniard, a two-time Grand Slam champion, outplayed the Latvian 6-7 (4-7) 6-2 7-6 (7-1).
Sevastova served for the match in the final set but Muguruza found a fine winner to break, before going on to dominate the tie-break.
"These matches are the ones that really count," Muguruza, 25, said.
"It's long, it's difficult, you have match points against you, you don't lose your courage, you don't lose your enthusiasm. And it worked today."
All four group winners at the 12-player event reach the semi-finals.
Earlier, France's Caroline Garcia beat Aryna Sabalenka 6-4 6-4 but narrowly missed out on qualification after losing her opening round-robin match.
Australia's Ashleigh Barty and German defending champion Julia Goerges secured their places in the last four on Thursday.