Murray lost the dispute, and the match. The pivotal ruling helped Djokovic win 7-5, 6-3 in the quarterfinals of the Sony Open.
The point in question occurred at the start of the 12th game, with Murray serving at 5-6. Djokovic charged forward to volley a short ball and hit it for a winner.
Murray argued -- and TV replays confirmed -- he should have be awarded the point because Djokovic's racket was on the far side of the net when he hit the ball. Chair umpire Damian Steiner declined to change his call, and such rulings can't be appealed for video review.
An irritated Murray briefly discussed the matter with Djokovic.
"I went and asked Novak, and he told me he was over the net," Murray said.
"Look, it might be my mistake," Djokovic said. "I think I crossed the net with the racket. I didn't touch the net. Maybe the rule is that you are not allowed to pass on his side with the racket. I'm not sure. You tell me."
That is indeed the rule.
A flustered Murray committed unforced backhand errors on the next three points to lose the game and the set.
"Obviously, that distracted him mentally, and after that he gave the set away," Djokovic said.
Murray took a lead in the second set but lost the final four games and the last 12 points. Afterward, he downplayed the bad call.
"I'm not angry," he said. "It maybe had a slight bearing on that game, but I was still up a break in the second set."
Djokovic, bidding for his fourth Key Biscayne title, will play Friday against the winner of the match Wednesday night between Roger Federer and Kei Nishikori.
Dominika Cibulkova erased three match points in the second set -- one when a call was overturned via replay -- and beat Agnieszka Radwanska 3-6, 7-6 (5), 6-3. In Thursday's semifinals, the No. 10-seeded Cibulkova will play the winner of the match Wednesday night between No. 2 Li Na and No. 11 Caroline Wozniacki.
Murray won the Key Biscayne title in 2009 and 2013 but wasn't at his best against Djokovic. The Scotsman committed five double-faults and 32 unforced errors, including a flurry down the stretch.
He took a 3-2 lead in the second set with his only service break, then double-faulted twice to give it right back.
But it all might have been different if not for the call that made one point stand out from the other 125. Djokovic had won praise for his sportsmanship when he conceded a point following an erroneous call in his match Tuesday, but against his good friend Murray, he left the verdict to the umpire.
A sideline reporter told Murray that TV replays showed he was correct about the call, and during the ensuing changeover he questioned Steiner.
"His racket was over the net," Murray said. "It's quite clear. You can see it on the replay."
"I have to make a decision at the moment," Steiner replied.
Any hard feelings on Murray's part didn't carry over after the match, when he shook hands with Djokovic and Steiner.
"It's a hard one for the umpire to call," Murray said. "Just frustrating."
Djokovic said he would have conceded the point if he had been clear about the rule.
"It's not my fault," he said. "Obviously, chair umpire didn't make the decision. I mean, I was never lying on the court. I always try to be fair to whoever I play against."
Cibulkova won despite losing her serve 10 times, double-faulting eight times and committing 51 unforced errors. There were 11 breaks in the first 12 games of the match.
Cibulkova collapsed to her back in jubilation when Radwanska's final shot sailed out. The runner-up at the Australian Open in January, Cibulkova advanced to the Key Biscayne semifinals for the first time.
Former No. 1 Martina Hingis and Sabine Lisicki overcame three match points against Anabel Medina Garrigues and Yaroslava Shvedova to win 3-6, 7-6 (7), 10-7 and reach the semifinals in women's doubles.
