The Scot beat 53rd-ranked Karen Khachanov of Russia 6-3, 6-4, 6-4 on Court Philippe Chatrier in two hours and four minutes, booking his spot in the Roland Garros quarters for the seventh time.
"I think today was probably the best I have played overall," Murray said afterward. "It was difficult conditions. It was pretty windy out there and wasn't easy. Each match I feel like I played better. I have hit the ball cleaner and started to see the right shots at the right moments. I've come a long way the past 10 days or so."
The three-time major champion is now 650-181 for his career, a .782 winning percentage. Murray is the 15th player in ATP World Tour history to reach the milestone.
Murray finished the match with 29 winners and just 14 unforced errors. The 21-year-old Khachanov, who was the youngest man left in the field, had 38 unforced errors.
"It's never fun to lose a match," Khachanov said. "But I take great experience from this match and playing on the Center Court. All the credit to Andy."
Murray will next play eighth-seeded Japanese Kei Nishikori, who recovered to beat Fernando Verdasco of Spain 0-6, 6-4, 6-4, 6-0 in the fourth round.
Murray leads Nishikori 8-2 in their head-to-head matches and won their lone clay-court clash at the 2015 Madrid Open.
"Kei is dangerous off both wings," Murray said. "Moves well."