Murray needed all his determination to see off the Frenchman
Andy Murray set up a semi-final with Mario Ancic in the World Tennis Tournament after Marc Gicquel retired while trailing 7-6 (7-2) 4-6 3-0.
France's Gicquel, ranked 55, pushed Murray all the way before he was forced to quit with a thigh injury.
Top seed Rafael Nadal later won a gripping battle against Jo-Wilfried Tsonga of France, 6-4 6-7 (5-7) 6-4.
The Spaniard goes on to play Gael Monfils, who beat fellow Frenchmen Julien Benneteau 7-6 (7-4) 6-1.
"This was a completely different match from my first two - today I played my best tennis so far in Rotterdam," said Nadal.
"I played against a very good opponent who showed form by winning a tournament (in Johannesburg) last week.
I kept him running and got a few loose errors. I'm happy with how I played
"Tsonga has an unbelievably good service. It was really heavy."
Murray was sharper than in his second-round tie and took the first set against Gicquel on a tie-break in Rotterdam.
Gicquel's tactic of rushing to the net frequently paid dividends but after he injured his thigh just before taking the second set, Murray assumed control.
The 21-year-old Briton later paid tribute to his opponent after a match that lasted almost two hours.
"It was a very good match, we both played pretty well," he said. "It's sad it had to end this way.
"I was hitting the ball well, I had opportunities on my serve, but he served well also and made it very difficult for me.
"I was able to dictate a lot of the points. I kept him running and got a few loose errors. I'm happy with how I played."
After Murray overcame Andreas Seppi in stuttering fashion on Thursday the Scot looked a little livelier and in the mood to exhibit his skills in what turned out to be an entertaining quarter-final.
It was a very steady opening set from both players with neither willing to take too many risks and it was no surprise it went to a tie-break.
Gicquel, who earned his place in the main draw of the tournament as a lucky loser after Robin Soderling pulled out, served strongly throughout but Murray dominated the tie-break.
The Frenchman then adopted a more aggressive strategy by coming to the net on a regular basis and, with Murray forced onto the back foot, the outsider took the match into a deciding set.
However, this did not come without a cost as Gicquel needed treatment on a thigh injury after landing awkwardly at the end of the second set.
Murray looked invigorated and started to push his struggling opponent to all corners of the court and, after losing the first three games without much of a fight, Gicquel had to call an end to the proceedings.
The British number one now goes on to face Ancic for the fifth time, with the big-serving Croat - who beat Mikhail Youzhny 6-4 6-2 earlier on Friday - having won three of their four previous meetings.