NEW YORK — Gael Monfils follows his own rules.
The guy does things on a tennis court no one else has — or can. Just search his name on YouTube and watch any of many video clips showcasing his speed and agility; start with the parallel-to-the-ground, a-few-feet-in-the-air dive at this year’s French Open.
He sips soda during breaks in his matches, raising the can in a toast to his agent.
He is currently without any coach at all, in an era when some players have two.
What Monfils has never done, despite all his talent — and in some cases, because he has appeared to value style over substance right there on court, in the middle of a point, preferring the spectacular to the sufficient — is reach a Grand Slam final. He took a step closer Tuesday at the US Open during a surprisingly matter-of-fact 7-5, 7-6 (8-6), 7-5 victory in the fourth round over No. 7-seeded Grigor Dimitrov, a man considered one of the sport’s up-and-comers.
There is a narrative building around the 20th-seeded Monfils’s success so far this year at Flushing Meadows, where he hasn’t dropped a set en route to reaching the quarterfinals for the first time since 2010: He has matured, is playing more carefully, more seriously.
The Frenchman, who will face Roger Federer for a spot in the semifinals, rejected that notion after Tuesday’s win.
‘‘I'm the same. So I will say I'm a bit more lucky than I was maybe sometime in the past. I think I haven’t changed a lot, to be honest. I haven’t changed a lot,’’ Monfils said. ‘‘I just play maybe solid today, but I'm still the same.’’
Federer advanced to the US Open quarterfinals for the 10th time in 11 years by eliminating 17th-seeded Roberto Bautista Agut, 6-4, 6-3, 6-2. Federer won the point on 35 of 52 trips to the net.
The other quarterfinal matchup on that half of the draw will be No. 6 Tomas Berdych against No. 14 Marin Cilic. Berdych beat 20-year-old Dominic Thiem, 6-1, 6-2, 6-4; Cilic was a 5-7, 7-6 (7-3), 6-4, 3-6, 6-3 winner against No. 26 Gilles Simon, who was treated for a back problem early on.
In women’s quarterfinal action Tuesday, 39th-ranked Peng Shuai of China ended the precocious run of 17-year-old Belinda Bencic of Switzerland, 6-2, 6-1. Peng’s next opponent will be No. 10 Caroline Wozniacki, who moved into her first Grand Slam semifinal in three years, overwhelming 13th-seeded Sara Errani of Italy, 6-0, 6-1, in a wind-whipped match.
The match began competitively enough, with points lasting 22 and 23 strokes in the first game, and Errani earning four break points before 2009 US Open runner-up Wozniacki eventually held.
Wozniacki wound up with a 26-12 edge in winners.
Peng, 28, advanced to her first Grand Slam semifinal in the 37th major tournament of her career; only five women took longer to get to the final four at one of the sport’s top four events.
Top-seeded and No. 1-ranked Serena Williams, who faces 11th-seeded Flavia Pennetta in a singles quarterfinal Wednesday, lost in the doubles quarterfinals with her sister Venus. Serena had her right ankle retaped during a medical timeout and later double faulted on the last two points in a 7-6 (7-5), 6-4 loss to the fourth-seeded Russian duo of Ekaterina Makarova and Elena Vesnina.
Serena and Venus are 4-3 in doubles in 2014, with two of the losses against Makarova and Vesnina.
The Williams sisters declined to speak to the media after the doubles match, but Serena told a WTA spokesman that she simply needed to have the tape on her right ankle redone and there was no injury issue.