Rafael Nadal avenged a fresh loss to a fellow Spaniard and Serena Williams set up a showdown with the reigning Indian Wells champion at the ATP and WTA hardcourt tournament on Tuesday.
Nadal saved five set points to finish off a two-set victory over Fernando Verdasco 6-0, 7-6 (11-9) in the third round on the main stadium court.
World number one Williams routed 70th ranked Kateryna Bondarenko 6-2, 6-2 to reach the quarter-finals at Indian Wells, one of the biggest events on the tennis calendar outside of the four Grand Slams.
Men's top seed Novak Djokovic, who is aiming for his third straight and a record fifth overall Indian Wells crown, defeated Philipp Kohlschreiber 7-5, 7-5 in the night match.
Djokovic advanced to the fourth round of the hardcourt ATP and WTA tournament, where he will face Feliciano Lopez who beat Roberto Bautista Agut 7-6 (7/5), 6-7 (10/12), 6-4.
Nadal, the nine-time French Open champion who turns 30 in June, avenged his first-round loss to Verdasco at the Australian Open in January.
Nadal moved a step closer to a fourth trophy in the California desert, where he took the title in 2013, 2009 and 2007.
The swashbuckling Spaniard next faces German Alexander Zverev who defeated Gilles Simon in straight sets 6-2, 6-2.
Nadal, who is seeded fourth, roared through the first set without dropping a game, but Verdasco came to life in the second, eventually forcing a tiebreak.
Nadal fought off five set points before clinching it when Verdasco hit a backhand long to end the one hour, 41 minute contest.
"It was a tough match, but I resisted," said Nadal, who broke Verdasco five times. "I lost a few matches this year that I had a chance to win so I need to play more matches like this."
Verdasco wasn't going down without a fight. Serving in the tiebreaker -- and down 6-7 on match point -- he challenged an out call and won, reversing the judge's call and allowing him to level at 7-7.
Nadal improved to 15-3 overall against Verdasco but they have had some memorable contests since their first encounter in 2005 in Doha.
They played a brilliant three tiebreaker match at Cincinnati in 2011, went five sets in the semis of the 2009 Australian Open, and earlier this year they played another five setter in Melbourne with Verdasco handing Nadal just his second ever first-round defeat in a Grand Slam.
"I have to go through these things," said Nadal. "In these kind of matches I have more to lose than him, so he's able to play very aggressive.
"He has amazing shots. When he arrives at a tiebreak, you know you're in trouble."
Williams, who is playing here for just the second time since ending her 14-year Indian Wells boycott, will face Simona Halep in the quarter-finals.
Last year at Indian Wells, Halep won their semi-final without even striking a ball after Williams pulled out of the tournament at the last minute with a knee injury. Halep went on to win the title.
That withdrawal cut short Williams' first Indian Wells campaign since 2001, when spectators booed her during the final and jeered her sister, Venus, and father Richard Williams when the pair arrived to watch the match. Richard Williams alleges he heard racial taunts.
Williams said she is grateful that the boos have turned to cheers.
"Every time I step on the court people cheer for me. It is just a different feeling," Williams said following her win over Bondarenko.
Halep moved on to the quarter-finals when her opponent Barbora Strycova retired in the second set with a respiratory problem.
Williams has dominated Halep over the years, beating her six times in seven matches. Halep's best moment against her was a straight sets win, 6-0, 6-2, in 2014 in Singapore.
"I like her game. She's a fighter. She killed me at one point so I will have to be ready," Williams said of facing Halep on Wednesday.
Japan's Kei Nishikori won his third round match Tuesday defeating Steve Johnson 7-6 (8/6), 7-6 (7/5).
World number six Nishikori next faces ninth seeded American John Isner who beat France's Adrian Mannarino 6-4, 7-6 (7/4).
Elsewhere on the women's side, like Halep, Magdalena Rybarikova of Slovakia advanced when an opponent stopped playing mid-match. Italian ninth seed Roberta Vinci was down 6-2, 2-0 when she called it quits because of an ankle injury.
Rising Russian star Daria Kasatkina continued her superb run this week by upsetting 12th seeded Timea Bacsinszky 6-4, 6-2 to reach the quarter-finals.
The 18-year-old is the lone teenager left in the women's field.