Murray did enough to keep his nose in front throughout, while the giant Argentine was unable to reprise the heroics that saw the pair produce such magic in last year's Rio Olympics gold medal match.
While Murray won that affair too -- and their only previous grand slam meeting -- Del Potro had triumphed in their most recent clash, so the Scot had been alert to the dangers.
"Yeah, it was obviously an important win for me and a big match, because Juan, when he's playing well, is one of the best players in the world," Murray said.
"To be playing him this early on in the slam is obviously not easy, but it can be a very positive thing.
"You play someone that good, maybe you're a little bit more switched on. Your focus is maybe a little bit higher."
Del Potro, whose career has been blighted by a recurring wrist injury, needed a good start against the world number one, but when he lost a tight first set tiebreak, the stage was set.
Losing that opener on a disputed linecall cut Del Potro deep. Murray jogged to his seat at the changeover, the Argentine stood at the net, bent at the waist, his head resting on the netcord. There he stayed until the umpire called time.
"I couldn't believe that set, that I lost that set, because I had many opportunities to win," Del Potro said. "I have been playing great, great points during whole, the first set.
"But this happens when you play against the No. 1 in the world or a great champion as Andy or Rafa (Nadal) or Roger (Federer) or these guys. You never know when you can win a set or a match, and that happened today."
The pair traded blows in the second set with Murray creeping ahead. But a monumental effort by Del Potro saw him break back for 5-5, only to instantly drop serve again as Murray yanked him around the court with tight angles, drop shots and lobs.
This time the Scot would make no mistake and crunched it out with his fourth ace of the match.
Del Potro's spirit was broken, and the vocal Paris crowd were quelled.
With some exquisite returning and acutely angled groundstrokes, Murray raced through the final set to set up a fourth-round clash with either American 21st seed John Isner or Russian Karen Khachanov.
(Editing by Pritha Sarkar)
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