The Serb did not need to be at his brilliant best to dispatch the world number 29 who laboured to stay in the match, but never looked like troubling his opponent.
After a short rain delay, Djokovic broke decisively in the 10th game of the first set and sprinted through the second on fast forward.
Mayer held on to the Serb's coat tails in the third, but Djokovic broke in the ninth game and finished him off with an ace.
"It took me a while to get used to the conditions, having played my last three games indoors," Djokovic said in a courtside interview.
"It was a little windy, but I'm satisfied with the overall performance. Florian had some opportunities to come back in the third set, as well as chances in the first, but I held my nerve at the important moments."
Djokovic will now face 16-times grand slam champion Roger Federer after the Swiss dismantled Mikhail Youzhny.
"It's always a pleasure playing against Roger, so I'm looking forward to that," Djokovic said.
"He's been so dominant and consistent in Grand Slams, it's the ultimate challenge on a grass court."