Following four-set victories over Andrey Kuznetsov and Martin Klizan, the Scot took down Juan Martin Del Potro 7-6 (8), 7-5, 6-0 during third-round action on Saturday afternoon.
However, the Spaniard did receive two time violation warnings during the match from Carlos Ramos, the same umpire who incensed Novak Djokovic by enforcing a similar penalty in the Serbian's third-round victory over Diego Schwartzman.
"I think it's going to be a good match and good experience for me".
"Obviously the first set was very important", said Murray. It was very slow and heavy conditions and to be coming back was hard.
As Del Potro, who said his troublesome groin did not affect him, put it: 'Andy, he's very smart on court, you know. Murray, 30, kept his nose in front throughout, while the giant Argentinian was unable to reprise the heroics that saw the pair produce such magic in last year's Rio Olympics gold medal match. Del Potro had four set points in total and double-faulted at 7-6 up in the tie-breaker. The importance of the first set was illustrated by the 45 seconds Del Potro spent leaning over the net with head in hands after his final forehand curled just wide.
Radwanska had won seven of their eight previous matches, including the only one on clay at the French Open nine years ago but was never in contention this time. He has not played amazingly in the first two matches but he is winning - that is what matters at the start of a tournament.
When asked why he kept putting his finger to his lips, Murray said: "I don't know why I was doing it". It's not new. past year I had some problems with my groin.
Del Potro, who went on to guide Argentina to their first Davis Cup title, was always going to be a danger lurking for one of the top seeds as he continues to work his way back up the rankings after wrist problems nearly ended his career.
Del Potro was the 2009 U.S. Open champion.
Kevin Anderson matched his best run at Roland Garros by reaching the last 16 on Saturday with a five-set win over Britain's Kyle Edmund.
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.
Martic is ranked 290th but she took just 49 minutes to beat the Latvian and match her best performance at a Grand Slam tournament. "We will try to give them a good show, a good game".
Meanwhile, 2014 runner-up Simona Halep eased through to the last 16 with a 6-0, 7-5 win against 20-year-old Russian Daria Kasatkina.
"It's nice to be in Paris in the fourth round", Halep said on Court Suzanne Lenglen moments after her win. I can run, I can slide everywhere.
Andy Murray can start to look ahead at the French Open after defusing the power game of Juan Martin del Potro to reach the fourth round.
Andy Murray celebrates during his third round match against Juan Martin Del Potro.
There was still time for the standing ovation that has become customary when Del Potro exits a tournament, with the Parisian crowd understandably delighted to see the popular Argentine back in their hometown tournament.