Murray started in the same vein, breaking Del Potro at the start of the third an this time ploughing on as he denied Del Potro a chance of a game at all in the third. Murray jogged to his seat at the changeover, the Argentine stood at the net, bent at the waist, his head resting on the net cord.
Chair umpire Carlos Bernardes called the linesman out to identify the mark.
The world No. 1 was a break down in the opener and saved several set points before clinching a lengthy tiebreak, which left Del Potro hanging on the net in frustration.
"I couldn't believe that I lost that set, because I had many opportunities to win", he said.
Murray seized his lifeline, a fourth ace giving him a two-set lead. It's been 15 years since Williams' first and only other visit to the French Open; her sister Serena Williams came second place in the 2016 Women's French Open, but sat out the competition this year due to her pregnancy.
3 - times Simona Halep has now made the Roland Garros fourth round in eight appearances.More news: UK's May grilled by voters, urged to confront Trump on Paris
"I thought I played some good tennis towards the end, but I expected a very tough match".
Playing his first Roland Garros since 2012, Del Potro walked off Court Philippe Chatrier to a roaring standing ovation - one the notoriously tough French crowd wouldn't give to just anyone.
The first set was massive, and the Argentinian's despair was caused by him knowing it was a long way back in the prevailing cool and heavy conditions. "I didn't feel good". "I had struggled the last six or seven weeks coming in".
Having twice stopped his opponent from taking the opening set, Stan Wawrinka dispatched Fabio Fognini like a gentle breeze does humidity, winning 7-6, 6-0, 6-2 to advance.
Murray next faces the victor of the match between American John Isner and Russian Karen Khachanov which will be played at a later time.
Seventh seed Marin Cilic established himself as a contender for the French Open title after sweeping past Feliciano Lopez 6-1 6-3 6-3 on Saturday to reach the last 16 without dropping a set.More news: Man Utd cool interest in Griezmann
This is likely to be recalled as the day Murray officially joined the party in a tennis season of two men.
"It took me five years, three surgeries in my wrist to come back, five years to come back and live these exceptional moments once again".
"So I need to respect that and work hard in practice and concentrate and if I do that, hopefully I can keep going further".
It was disappointment, however, for British number two Edmund, as he lost out to Kevin Anderson in five sets.
Spaniard Fernando Verdasco also got through with a much quicker 6-2, 6-1, 6-3 win against No. 22 Pablo Cuevas of Uruguay.
The beaten finalist at Roland Garros a year ago doubled his lead after needing two opportunities to serve out the second set, before a faultless display in the third subdued a leg-weary Del Potro.
French Alize Cornet registered a 6-2, 6-2 victory over world No. 8 Polish Agnieszka Radwanska in an hour and 19 minutes, marching into the fourth round.More news: Cristiano Ronaldo bags brace as Real Madrid clinch Champions League
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