Petra Kvitova is back in the BNP Paribas Open quarterfinals for the first time in seven years, but she had to get there the hard way.

The two-time Wimbledon champion Kvitova had to save four match points before battling past No.3 seed Jessica Pegula 6-2, 3-6, 7-6(11) in a Round of 16 matchup on Tuesday.

Kvitova, the No.15 seed who previously reached the Indian Wells quarterfinals in 2013 and 2016, needed 2 hours and 14 minutes to outlast Pegula in a topsy-turvy affair on Stadium 1.

"Just kept going," Kvitova said afterward, recalling the match. "I just tried to still be aggressive, but it not always was there for me. The emotions were of course very happy. And a little bit exhausted now."

Kvitova now holds a commanding 4-1 head-to-head lead over Pegula, and she has beaten the World No.3 both times they have played this season. Kvitova defeated Pegula at United Cup in January, only days before Pegula upset World No.1 Iga Swiatek at the team event.

Sunshine surge: Making her 12th appearance in Indian Wells this year, another win for the 33-year-old Kvitova would be a breakthrough. she has never reached the BNP Paribas Open semifinals.

In fact, Kvitova has never reached a semifinal at either of the "Sunshine Double" events -- she has lost three times in the Miami Open quarterfinals as well.

But Kvitova has played her best against the best of late -- she is 4-0 in her past four matches against Top 5 opposition.

Key moments: The first set was all Kvitova, where she won 16 of her 20 service points and never faced break point. However, Pegula battled back in the second set, where she reeled off 12 of the last 13 points.

Pegula broke Kvitova at love in the first game of the third set as part of a 14-point winning streak, and she kept herself ahead during the back-and-forth decider up to 5-4, where she held her first match point.

Kvitova, though, erased that chance with a blistering forehand winner, and the Czech used a strong forehand return to level matters at 5-5. Pegula moved ahead by a break once more at 6-5, but Kvitova broke back immediately to queue up the tiebreak.

In the breaker, Pegula had match points at 6-5, 8-7 and 11-10, but Kvitova used her power game to swat away each of those opportunities with winners. Kvitova also saw her first three match points fended off by Pegula, but she converted her fourth by catching the sideline with a volley winner.

Showdown with Sakkari: Kvitova's quarterfinal opponent will be last year's runner-up Maria Sakkari. No.7 seed Sakkari also came through a closely contested three-setter on Tuesday, moving past No.17 seed Karolina Pliskova 6-4, 5-7, 6-3 to make the quarterfinals.

After the pair split the first two sets, Pliskova won a 19-minute game, where she survived 11 deuces and saved 10 break points, simply to hold for 1-0 in the third set. Czech Pliskova briefly ran with that momentum, breaking Sakkari directly afterward for 2-0.

But Sakkari broke back immediately to pull back on serve, and the Greek eased home from there, winning six of the last seven games of the encounter and leveling their head-to-head at three wins apiece.

Desert rematch: Sakkari has a 4-3 head-to-head lead over Kvitova. Their most recent meeting was here at Indian Wells last year, where Sakkari dispatched Kvitova 6-3, 6-0 in the third round.

"I expect a big fight, for sure," Kvitova said. "That's normally [what] our matches look like. And I know that she's playing all three-setters here, as well as me, probably, so it will be a really close one, for sure.

"I know what I have to play. I know I lost to her here in Indian Wells. ... I just will try my best to play aggressive as I did today."