Former world No.1 Daniil Medvedev was at his ruthless best in thrashing American Tommy Paul to reach the quarter-finals at the ATP event in California.

In a late-starting match after several rain delays throughout the day, Russian fifth seed Medvedev moved into the last eight with a 6-4 6-0 win over the 10th-seeded American at Indian Wells on Tuesday (Wednesday AEDT).

Medvedev needed only 12 minutes to claim the opening four games, then recovered from a brief dip during the roller-coaster opening set to ease through.

A double break in the second set gave the Russian the momentum he needed to close out the victory and book a match-up with Frenchman Arthur Fils, who got past American Marcos Giron 6-2 2-6 6-3.

Holger Rune, the 12th seed, secured a 6-4 6-4 victory over eighth-seeded Stefanos Tsitsipas to end the Greek's seven-match winning streak.

The Dane delivered the shot of the tournament to stave off a break point in the second set, producing an arcing 'tweener from behind the baseline, sending the ball to the opposite baseline that an outstretched Tsitsipas was unable to retrieve.

"I stayed very committed on my game plan and mentally I was very good,'' Rune said.

"That made the difference, how composed I could start, because Stef is back in shape I think it is fair to say. It was a cool battle.''

Rune next meets Dutchman Tallon Griekspoor, who earlier defeated Japanese qualifier Yosuke Watanuki 7-6 (7-4) 6-1 to reach his first Masters 1000 quarter-final.