The British seventh seed, who next faces Spanish left-hander Fernando Verdasco and was a semi-finalist in 2011, had been level at 7-7 with the German 28th seed when the match was halted on Saturday night. (Agencies)
When the pair reappeared, Murray squandered a match point at 9-8 but wrapped up the match in the 22nd game of the decider in a clash which featured 18 breaks of serve and 123 unforced errors.
It was the longest fifth set of Murray's career and the first time he had been taken the full distance since defeating Verdasco in last year's Wimbledon quarter-finals.
"Last night was tough for me as I did a lot of running, so under the circumstances we both played some good points. It was a pretty high standard," he said.
The 30-year-old Verdasco, seeded 24, reached the fourth round for the first time since 2010 with a 6-3, 6-2, 6-3 win over France's 12th seed Richard Gasquet in another third round tie held over from Saturday.
Verdasco said last year's Wimbledon clash against Murray, where he won the first two sets, will have no bearing on Monday's fourth round showdown.
"Every match is different. You can't compare a match in Wimbledon when he was playing home on grass with a match here in Paris," said Verdasco.
"And it doesn't mean I'm going to win. Maybe he's gonna win in three sets. All I'm saying is it's a totally different match."
Czech sixth seed Tomas Berdych made the quarter-finals for the second time with a 6-4, 6-4, 6-4 win over America's 10th seed John Isner.
Berdych was a semi-finalist in 2010, beating Isner on the way in straight sets in the third round.
Isner was bidding to become the first American man to reach the quarter-finals in Paris since Andre Agassi in 2003 but he was out-served by 28-year-old Berdych who hit 11 aces to his opponent's seven.
"There were quick breaks in each of the sets. That's something which really helps through all the match, especially with a guy like John. He likes to stay as close as possible, serving well. It's a good thing to avoid playing the tiebreaks with him," said Berdych.
Berdych will next face either fourth seed and 2009 champion Roger Federer or explosive Latvian Ernests Gulbis for a place in the semi-finals.
The British seventh seed, who next faces Spanish left-hander Fernando Verdasco and was a semi-finalist in 2011, had been level at 7-7 with the German 28th seed when the match was halted on Saturday night.