Top seed Sofia Kenin admitted "being a Grand Slam champion" proved crucial as she saved a match point to reach the quarter-finals of the season-opening Abu Dhabi WTA tournament on Sunday.
The defending Australian Open champion defeated 13th-seeded Yulia Putintseva of Kazakhstan 3-6, 7-6 (7/5), 6-4.
However, Kenin, who was also last year's Roland Garros runner-up, had to save a match point in the 12th game of the second set to stay alive.
She will now face ninth-seeded Maria Sakkari of Greece for a semi-final spot.
Sakkari defeated fifth-seeded Garbine Muguruza, the former Wimbledon and Roland Garros winner, 7-5, 6-4.
"I practice with her (Putintseva) quite a bit, and I know her game well, and she knows my game pretty well," Kenin said during her post-match press conference.
"I guess it helps being a Grand Slam champion, knowing kind of what to do on those tough points, those tough moments, and I was able to find my rhythm by the end of the third set."
Ukraine second seed Elina Svitolina came from 3-5 down in the final set and saved two match points during the final-set tiebreak to beat 17th-seeded Ekaterina Alexandrova of Russia, 6-2, 6-7 (7/5), 7-6 (10/8).
Alexandrova fired 40 winners although they were outweighed by 57 unforced errors.
Svitolina will next face another Russian, Veronika Kudermetova who saw off Spain's Paula Badosa 6-4, 4-6, 6-1.
"She was striking the ball really well," Svitolina said.
"It was really tricky for me to come back from being 3-5 down. I was just trying to be focused on every point and not let this match take away the good tennis that I played in the first set."
Monday's other quarter-finals see fourth seed Aryna Sabalenka face Elena Rybakina, the sixth seed, and Marta Kostyuk of Ukraine tackle fellow unseeded player Sara Sorribes Tormo of Spain.