The British No 1 dropped the opening set and was dragged into a second set tie-break, but yet again displayed his battling qualities to claim a 3-6 7-6 (7-2) 6-4 win at Queen’s Club.
Rattling down a deceptive serve, Muller forced his familiar foe on the back foot in the early stages and snatched a break when Murray fired a forehand into the net.
The two men had trained alongside each other in their formative years, but Muller’s serving had no doubt developed into a more telling weapon and he fended off break points with thudding deliveries.
Murray could not claw himself level and the Luxembourg man confidently took the first set, drawing a concerned hush from the home crowd.
The atmosphere became increasingly fraught as Muller refused to give ground in the second, taking Murray into a tie-breaker and another duel with that troublesome serve. ??
But while others would exercise caution, Murray attacked with defiant ambition and opened a 5-2 lead following a framed smash from Muller, before levelling the match just moments later.
Suddenly Murray was bouncing up and down, filled with an energy instilled by fresh confidence, and he broke Muller at the start of the third set with a fizzing forehand.
The Scot sensed that his opponent was wilting and he brought up match point with a forehand into the open court after a scampering rally.
He quickly sealed a place in the semi-finals when Muller slashed his return into the net and the world No 3 remains on course for a fourth title. ??