Tempers frayed in the seventh game of the third set after Verdasco's serve was called out as he was heading back to the chair for the change of ends.
The left-hander asked umpire Pascal Maria to call in the supervisor to deal with the rumpus, before Murray conceded the point, keen to move on in a fast-paced match.
"He missed...the return because my serve was to the line and he couldn't hit it with the strings," Verdasco told reporters after losing 6-4 7-5 7-6(3).
"So it was completely out of sense to serve a first serve again. I said to call the supervisor, and Andy said that it was fine, and it was a point for me."
Nursing the grudge as well as licking his wounds at failing in his bid to reach the Paris last eight for the first time, Verdasco said run-ins with Maria were nothing new.
"He's not the kind of umpire I get along with. I can tell you that," he bristled.
On court, Verdasco's blast at the umpire fired him up to break back but seventh seed Murray regrouped to prevail in a tiebreak, having shown flashes of speed and touch throughout the match.
Wimbledon champion Murray played down the incident, telling reporters: "It was a great serve and I mis-hit the ball. It didn't go in. Yeah, I gave him the point."
The Briton said the two-day fifth setter in the previous round against Philipp Kohlschreiber - including a 96 minute 12-10 final set which was the longest decider Murray has played - had drained him.
"I was tired after the match against Kohlschreiber. It was a long match. It was mentally draining as well when you don't have that day to recover and you're coming back on court 7-all," he said.
Verdasco had also finished his delayed third-round match on Sunday after fading light curtailed play on Saturday.
Asked if it was his best performance of the tournament, Murray said courtside: "I think so. (It was an) unbelievable atmosphere today, I really enjoyed myself on the court. We played some great points and he fought extremely hard in the third set."
Murray, still without a coach since splitting with Ivan Lendl in March, will play French showman Gael Monfils for the chance to reach the semi-finals at the clay grand slam for the first time since 2011.
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