It proved to be a match with very little to separate the duo as world number three Murray triumphed in two tie-breaks.
There was an injury scare for Murray in just the second game of the encounter. Having been made to stretch for a shot down the line, the Scot immediately grasped his hip.
However, despite the fact that he appeared to be in pain, he kept himself in contention and even spurned three break points in the eighth game. As it was, a breaker was required to determine a winner.
Neither player could make any telling impact during the opening exchanges, with both finding a mini-break hard to produce. It eventually went the way of Murray, who won through 13-11.
Germany's Mayer broke early in the second set, but his advantage was cancelled out by Murray when he reduced the arrears to 4-3. The remaining service games were then held as another breaker was reached.
On this occasion Murray claimed the imitative early on with a break, before going on to take it 7-3.