Roger Federer and Rafael Nadal stayed on course for a semi-final showdown in the desert after making the last eight at the BNP Paribas Open in Indian Wells on Wednesday.
Fourth seed Federer, who is chasing a record sixth title in the desert, breezed to victory against Edmund 6-1 6-4.
The Briton suffered a chastening first experience of playing the Swiss 37-year-old and although he gave a better account of himself in the second set, Federer was always in control and wrapped up the win in 63 minutes.
He was 5-0 down before he won a game, but Federer comfortably closed the set out. The second set was a closer affair, but Federer broke in the fifth game after a forehand winner down the line set up two break points.
Federer was tested in the final game as Edmund had three break points, but Federer saved them all and booked his place in a 13th Indian Wells quarter-final when Edmund sent a forehand into the net.
Next up for Federer is Poland's Hubert Hurkacz who continued his winning run having already knocked out Kei Nishikori by edging past Denis Shapovalov 7-6 (7-3) 2-6 6-3 to reach his first Masters 1000 quarter-final.
Nadal continued his ruthless form as he bombed down seven aces and his way to beating Filip Krajinovic 6-3 6-4.
The Spanish second seed lost his serve just once in the match on a sunny and windy Wednesday in California.
"The difference between players is not huge. It's small gaps," Nadal said about the upsets on Tuesday, including the surprise exit of world No 1 Novak Djokovic. "Is true that for the last 10 years didn't happen very often."
He'll face Karen Khachanov next after the Russian won the clash of Masters 1000 champions with John Isner 6-4 7-6 (7-1).
Japan's Yoshihito Nishioka was forced to retire injured after dropping the opening set 6-4 of his clash against 19-year-old Serb, ranked 130th in the world, Miomir Kecmanovic.
Kecmanovic became the first lucky loser to reach the last eight since the tournament achieved Masters 1000 status in 1990.
"It will be funny that somebody other than Novak is still in," Kecmanovic said of his famous countryman.
Hard-hitting Canadian and 2016 finalist Milos Raonic is next for Kecmanovic after he defeated Germany's Jan-Lennard Struff 6-4 6-3.
In the women's draw, 18-year-old Canadian wildcard Bianca Andreescu demolished two-time major winner Garbine Muguruza 6-0 6-1 in a 52-minute blow out to reach the semi-finals.
Next up for the world No 60 is a meeting with sixth-seed Elina Svitolina who beat 19-year-old Marketa Vondrousova in straight sets.
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