The second-seeded Federer hit 11 aces, won 76 per cent of his service points and converted two of his six break point chances to remain undefeated in four matches against Mayer.
“I'm very happy with the way things went today. I obviously knew playing against Mayer in the first round was going to be tricky,” Federer said. “He's in the Top 30 and has been to the quarter-finals of Wimbledon. And I've played him here on grass before, so I know how tough he can be.
“But I felt I was focussed, was moving well and bascially, didn't have any letdowns on my serve. I was able to create a few more chances than he did. I'm through with my first victory on grass this year and I hope it's not my last.”
Federer was playing his first match since falling to World No. 1 Novak Djokovic in the Roland Garros semi-finals. Federer has won four titles this season, in Rotterdam (d. del Potro), Dubai (d. Murray), Indian Wells (d. Isner) and Madrid (d. Berdych).
The 30-year-old Swiss, who signed a lifetime contract with the ATP World Tour 250 grass-court tournament in Halle, has a 37-4 event record, and is looking to collect his first trophy at the tournament since triumphing in 2008 over Philipp Kohlschreiber.
In the quarter-finals, Federer will clash with big-serving Milos Raonic. Federer has won both of their meetings this season in three sets, edging the Canadian in Indian Wells and Madrid.
