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The fifth seed, a finalist in California in 2023 and 2024, looked in real trouble when he trailed the 20 year-old Fils 2-4 in the third set. However, Medvedev has a history of delivering at the first ATP Masters 1000 event of the year and he did so once again to earn a 6-4, 2-6, 7-6(7) victory on his third match point.

"I lost a lot of tight matches this year where I could have won, should have won maybe. I have lost a lot of tight matches where it goes a little bit 50-50 and the more it goes like that, the more you can lose confidence in the tight moments," Medvedev said. "I was happy I was able to get over the line as he saved some match points and had a break lead in the third. I am just happy to win."

In windy conditions on Stadium 1, Medvedev produced a series of stunning passes against Fils, who regularly closed the net to pressure Medvedev. 

With nothing to separate the two, a deciding-set tie-break was left to determine the clash. Medvedev had won just one his past nine third-set tie-breaks but he played aggressively and consistently in the breaker to triumph after two hours and 24 minutes.

Fils threw everything at the fifth seed but crucially pushed a volley long when match point down at 8/9, with Medvedev leaping into the California air after earning a battling victory.

"The match was very tough due to the wind," Medvedev said of the conditions, which caused havoc in the third set. "It was tough to play tactically, technically. Whoever gets a bit more of a swirl of wind, they can frame it and it is a bit of luck. I knew that he had a break in the third and I knew I could break back and that is what I managed to do."

Medvedev holds a 20-7 record at the hard-court tournament and is aiming to lift his first trophy since 2023, when he clinched his sixth ATP Masters 1000 title in Rome. The fifth seed is into his 15th semi-final at this level and will try to reach his 11th final when he faces Holger Rune.

"He can play well. He is a top player," Medvedev said of Rune. "Maybe a bit up and down still as he is a young player. But when he is in the quarters or semis he is playing well."

Fils, who won 61 per cent (22/36) of his net points, was competing in his first ATP Masters 1000 quarter-final. 

The 20 year-old is up three spots to No. 18 in the PIF ATP Rankings and is set to rise to a career-high on Tuesday.