Alexander Zverev overcame Russian in five sets while Austrian Dominic Thiem downed Japan's Kei Nishikori in four sets.
Second-seeded Alexander Zverev has reached his first Grand Slam quarterfinal the hard way, beating Karen Khachanov 4-6, 7-6 (4), 2,6, 6-3, 6-3 on Sunday for his third straight comeback win in five sets.
The latest gritty victory came with the usual temper flare-ups from Zverev. But the German player also showed, once again, that he knows how to dig deep when it matters. In all three of his five-setters at Roland Garros he has trailed 2-1 in sets.
"I'm young. I might as well stay on court and entertain you guys," the 21-year-old Zverev joked with the crowd. "This definitely paid off, the hours in the gym every day ... Everything comes together slowly and I'm happy to be here."
Zverev says he spends up to four hours each day working on weights and fitness.
He might well need to up that schedule considering his quarterfinal opponent is No. 7 Dominic Thiem of Austria, who is one of the fittest players on the men's circuit and has reached the past two semifinals at Roland Garros.
"I'm expecting another five-set match. I'll get myself ready," Zverev said, smiling. "I'm very happy about being in the quarterfinals here going the hard way, going the long distance ... showing everybody that I can play for as long as I need to."
Almost 12 hours altogether so far.
Thiem, who has played three straight four-setters, beat No. 19 Kei Nishikori of Japan 6-2, 6-0, 5-7, 6-4 on Court Philippe Chatrier.
Nishikori won just 14 points in the first set and nine in the second, losing to Thiem for the first time.
The 24-year-old Thiem leads 4-2 overall against Zverev, but lost to him last month in the Madrid Masters final. Thiem called their upcoming quarterfinal "the matchup most of the fans in Germany and Austria were hoping for when they saw the (French Open) draw."
On Court Suzanne Lenglen, Zverev's smash at the net gave him match point, which he took when Khachanov netted a forehand.
Zverev sank to his knees in celebration. He then patted Khachanov, a friend from their junior days, sympathetically on the chest before pumping his arms in celebration.
As in the previous two rounds, Zverev was struggling for consistency. This was illustrated in the 10th game of the second set.
Zverev was serving for the set at 5-4, he soon trailed 0-40.
Then, in a blur Zverev won the next four points to give himself a set point — only to miss a smash from near the back of the court. An ace gave him another set point but he missed that one, too, putting a low volley into the net.
On his third set point, the erratic Zverev found the net again with a sloppy backhand. Khachanov punished him and broke for 5-5.
The second-set tiebreaker was scrappy, Zverev clinching it with an ace to level the match.
Zverev has youth on his side, but he has been spending long on court and his body is showing it.
At the start of the fifth set, he had a medical time out for treatment for an apparent blister on his left foot.
It did not seem to impede him, however.
He broke immediately for a 1-0 lead and jumped around on court, waving his arms to get the crowd going.
Former World number one Serbian Novak Djokovic eased past Spanish veteran Verdasco 6-3, 6-4, 6-2 and will play in the last eight at Roland Garros for a record 12th time.
The 12-time Grand Slam champion took the first two sets by a single break of serve and raced through the third as 34-year-old Verdasco ended with 48 unforced errors.
He will face Italian surprise package Marco Cecchinato in his 40th major quarter-final.
The world number 72, who had never won a Grand Slam match before this week, stunned Belgian eighth seed David Goffin 7-5, 4-6, 6-0, 6-3.
In women's play, 13th-seeded Madison Keys reached the quarterfinals for the first time at Roland Garros after beating No. 31 Mihaela Buzarnescu of Romania 6-1, 6-4 on Chatrier.
"I made the final of the U.S. Open but lost to my friend Sloane Stephens," Keys said. "Hopefully big things can happen here."
Keys next faces unseeded Yulia Putintseva of Kazakhstan, who beat 26th-seeded Czech Barbora Strycova 6-4, 6-3.
If she wins that match, Keys could meet Stephens in the semifinals.
The 10th-seeded American also reached the last eight in Paris for the first time, beating No. 25 Anett Kontaveit of Estonia 6-2, 6-0.
Stephens next plays either Australian Open champion Caroline Wozniacki — seeded second — or 14th-seeded Russian Daria Kasatkina.