In fact this was his first ever straight sets win against Del Potro, against whom he fought out an epic Rio Olympics final and then lost to in September's pivotal Davis Cup semi-final rubber. Later, Del Potro said, "I couldn't believe I lost that set", but added, "This happens when you play against the number one in the world".
World number one Murray triumphed 7-6 (10/8), 7-5, 6-0 for his 7th win in 10 meetings with Del Potro whose challenge fizzled out after squandering 4 set points in the 87-minute opener.
"I think that the relationship is not very good", said 27-year-old Cornet.
Del Potro lauded Murray's adjustments - new returning angles, more and more leg-sapping drop shots, even attacking the 6-foot-6 (1.98-meter) Argentine's forehand - as the match wore on, saying: "Andy is one of the smartest guys on the circuit, and he knew what my weak points were".
He has not had a great season so far, though, particularly on the clay-court circuit leading up to the French Open, but he now has reached the fourth round for the eighth time in 10 appearances in Paris.
In the women's singles action, third seed Simona Halep beat Daria Kasatkina 6-0, 7-5 and set up a last 16 clash with Carla Suarez Navarro. At the end of the first set, Del Potro slumped on the net, head down after squandering chance after chance.
Wawrinka also endured a tiebreak in the opening set against Fabio Fognini, where he set at 7-2, before regrouping himself to win 6-0, 6-2 in two sets to follow.
No deal yet between UK Conservatives and DUP to back PM May
After House Speaker John Bercow was re-elected without challenge, a chastened May quipped: "At least someone got a landslide". However, a deal with the DUP also risks destabilising Northern Ireland by increasing the influence of pro-British unionists.
Murray will face either John Isner or Russian Karen Khachanov in the next round at Roland Garros as the duo prepare to square off later on Saturday evening.
Wawrinka will meet the lone remaining Frenchman for a place in the quarter-final, facing either 15th seed Gael Monfils or 24th-seeded Richard Gasquet.
Anderson twice recovered from a set down to advance 6-7 (6/8), 7-6 (7/4), 5-7, 6-1, 6-4 in just under 4 hours in a duel between two players born in Johannesburg. "I'm working things out while I'm playing the matches, and that's a really, really important part of my game".
Next up for Djokovic is No. 6 Dominic Thiem of Austria - the player he beat in last year's semifinal in three sets, dropping just seven games.
Earlier on Saturday, No. 7 seed Marin Cilic advanced following a routine 6-1, 6-3, 6-3 win over Feliciano Lopez, and Murray's British compatriot Kyle Edmund fell out at the hands of Kevin Anderson. "I think that was the reality of it for me today".
The seventh-seeded Croat dropped his opening service game and then won eight straight games to take complete control against Lopez.
Alize Cornet and Caroline Garcia booked an all-French contest in round of 16, as the former shocked No. 9 seed Agnieszka Radwanska 6-2, 6-1, while the latter saw off Hsieh Su-Wei of Chinese Taipei 6-4, 4-6, 9-7.