The third-seeded Djokovic overcame hip, ankle and stomach ailments Tuesday to outlast Tommy Robredo 4-6, 6-2, 6-3, 5-7, 6-3.
Muller later became just the second qualifier since 1968 to make the quarters at this tournament, finishing off No. 5 Nikolay Davydenko 6-4, 4-6, 6-3, 7-6 (10) with the most exciting point of the day.
Muller flicked a shot that clipped the net and made it over, forcing Davydenko to hustle in. Davydenko’s return also hit the net, but the ball popped up and landed back on his side.
Davydenko spiked his racket in anger. Muller dropped his racket in relief, then the 130th-ranked player threw it into the crowd to celebrate.
“I think it’s not about that last point. It’s about many points. I had so many chances,” Davydenko said.
Earlier, fifth-seeded Elena Dementieva reached the semifinals, beating No. 15 Patty Schnyder 6-2, 6-3. No. 2 Roger Federer played in the late afternoon.
Popular for his impeccable impersonations of fellow pros, Djokovic gave a real-life imitation of someone who does his best when hurt.
“If I start talking about the things that are bothering me now, we can talk till tomorrow,” he said. “After the fourth set, I really doubted.”
Djokovic twice called for a doctor, and looked to be in serious trouble when he went to a fifth set against an extremely in-shape opponent. But with the score 2-all, the No. 15 Robredo tumbled onto the hard court while chasing a shot, and the Spaniard lost his zip.
Later, Robredo wondered how badly Djokovic was injured.
“Novak was doing the show,” Robredo said. “I had pain, as well, all over my body because I think I run a lot more than him, and I said nothing.”
“So did I trust him? No. I think he took his time because he was a little bit more tired and that’s a part of the game,” he said. “I think that if you’re not fit enough, then don’t play.”
Runner-up at the last U.S. Open and the Australian Open champion this year, Djokovic next takes on the winner of the Tuesday night match between No. 8 Andy Roddick and No. 11 Fernando Gonzalez.
“Whoever I play will be physically fitter than me, that’s for sure,” Djokovic said.
Djokovic is developing a history of coming up hurt at major tournaments. He quit because of an infected blister on a toe while trailing Rafael Nadal in a 2007 Wimbledon semifinal. He also stopped after losing the first two sets of his 2006 French Open quarterfinal against Nadal, citing a back injury, and retired during his second-round match of the 2005 French Open.
Djokovic struggled midway through this match and seemed to grow frustrated. At one point, he slung his racket after a missed shot, drawing boos and whistles from the crowd.
“Maybe they don’t like me anymore,” he said.
Noted for bouncing the ball up to 30 times before serves, he sped up his routine as the match went on, trying to get off the court quickly. Robredo often wouldn’t let him, engaging Djokovic in long rallies.
On a sunny afternoon with temperatures in the high 80s, Djokovic had enough energy in the end to raise his record to 8-3 in five-set matches. Robredo fell to 9-4 in them.
Muller is the best player to come from Luxembourg, but wants a lot more. After rallying from two-set deficits in his previous two matches, he joined Nicolas Escude in 1999 as the only qualifiers in the Open era to make the quarters at the U.S. Open.
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Davydenko, Robredo in Warsaw final
Text message to Müller: “Well done!”
“New life and real determination”
