The second-seeded Serbian will next play third seed Tomas Berdych after the Czech defeated another German, Philipp Petzschner 7-5 6-4.
Djokovic, bidding to win the title for the third successive year, was rocked by Mayer's early challenge, dropping his serve in the opening game and then fighting off two break points at 0-2 before holding on his fourth game point.
After changing his racquet during that game Djokovic then settled down and won his next three service games without losing a point. Down 4-5, he broke Mayer to love, held off a break point in the next game with an ace and then broke Mayer to love again to take the set.
The second set was far more straightforward. Mayer averted a break point in the second game but made a forehand error to fall behind 3-1 and Djokovic then dominated the rest of the match.
"It was a very slow start," Djokovic told reporters. "Quite different condition from last night's match. The ball was going faster today, and he took it to me from the start. Already first game he was on the net, twice, three times. You know, I was not moving my legs well.
"But when I needed to play well and needed to keep the ball in the court, I did. Match turned around since the break on 5-4."
Berdych had been stretched to three sets in his three previous matches with Petzschner, and he lost their last meeting in Munich last year, so he knew a difficult match was in prospect.
Four of the first five games went against serve, before Petzschner faced four set points on his own serve at 5-4. He survived that threat, and then held three break points of his own to lead 6-5.
This time it was Berdych who fought off the threat, before breaking to claim the set on his seventh set point when a strong return forced a backhand error.
Just one break decided the second set, when Petzschner netted a forehand 5-4.
"Of course I can improve on many things, especially my serve," said Berdych. "I'm struggling a little bit. You know, it could be the way of changing little bit from inside to outside. But I'm in the semis, so tough to complain about that."
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