Petra Kvitova has the fire in her eyes again. On a warm Friday morning on Arthur Ashe, she was back in her element, on the big stage her talent deserves, and, in two sets that lasted just an hour and a quarter, she showed no mercy to Caroline Garcia in what was one of the most clinical and impressive wins of the week.

Garcia, 19th in the world and once, famously, Andy Murray’s tip for the top, saved two match points in the ninth game of the second set, but could do little about Kvitova’s sixth and final ace, which wrapped it up 6-0, 6-4.

What a summer the 27-year-old Czech left-hander has had, on and off the court. Returning after the horrific knife attack in her own home before Christmas, she has somehow rediscovered much of the power and zip in her huge ground strokes, and is serving with pleasing consistency. Her first serve clicked well enough to return her a 76% strike rate, and she won 14 of 20 points on second serve (70%), which is where big matches are invariably won and lost.

Throughout the short match she maintained a steady gaze on her opponent, allowing her few opportunities to work her way into the match in a whirlwind first set, which lasted 25 minutes, and grinding it out in the second, which went 48 minutes. It was the sort of workout she needed for the tougher assignments ahead after a 59-minute blowout of Garcia’s compatriot, Alizé Cornet, although the former world No1 Jelena Jankovic had given her an hour and a half of her best in the first round.

Kvitova said courtside she was most pleased with “my serve and my movement around the court”, adding: “Caroline is very tricky, I know how she can play. I was trying to stay low and run.” It was more than just another win, however: just the 13th of her comeback, her 22nd at the US Open on her 11th visit, although she has never got past the quarter-finals, even in her pomp. So, given that history, she did not disguise her joy at making into the fourth round for the fifth time.

“It means a lot. I really appreciated this time today, to be in the fourth round. After everything I’ve been through it’s a very happy moment for me.” Asked about the inscription her team were wearing on their T-shirts in her box, she explained: “It means ‘Come on’ in Czech, to show how important it is for me to come back.”

Garcia, who allowed the qualifier Tereza Martincova only a single game in the first round and beat Ekaterina Alexandrova in three sets in the second round – did well to fight back after facing the prospect of complete embarrassment in the first set. She had reasonable expectations of winning, as well, having beaten Kvitova in the past two meetings, but those were too long ago to have much relevance on day five here.

Kvitova has never fulfilled her potential at Flushing Meadows but, in a draw that is shredded of its stars almost daily, she has as good a chance as any of going deep. Her best effort here was in 2015 when she took the first set off the eventual champion, Flavia Pennetta, before going out in three sets in the quarter-finals.

Hers has been a career of injuries, setback and drama – although she is hardly alone in that department. While away from tennis, she honed her communication skills and trained with tentative hope at Club La Santa in Lanzarote, spending much of her time over a chess board before launching herself back into the demands of the tour.

She reached the second round at Wimbledon, her first slam event back, and has struggled to find a rhythm elsewhere. Her six losses this year have come against players who would once have been awed by her presence alone, all of them on the outer fringes of the rankings at the time.

But she has longevity. Kvitova shares with the absent Serena Williams – who was going into labour almost as the Czech was coming off court on Friday – of winning at least one title every year on the tour since 2011. The American’s streak goes back to 2007, although she will not add to her tally this year.

Kvitova, like Williams, is a great survivor. She plays the game with a smile on her face, rarely complaining – even though she has had plenty of cause to do so over the past year or so. If she does advance past the quarter-finals this time, she will be rightly acclaimed and for all the right reasons.

Elsewhere in the early day matches, Pablo Carreño Busta, the Spanish 12th seed, made unusually short work of the French marathon man, Nicolas Mahut, winning 6-3, 6-4, 6-3 in and hour and 49 minutes on Louis Armstrong.