Federer needed just 61 minutes to seal the victory — abetted somewhat by Dodig’s six double-faults, the last of which came on match point.
The quick finish may have been a godsend for the Swiss great, who said he “tweaked” his back late in the match.
However, Federer said he fully expected to be fit enough to continue his pursuit of a first title of 2013. “I’m not too worried,” Federer said. “I have gone through it so many times where you feel a little tweak. You might play next day. Now this time around I have a day off, extra time.
“From that standpoint I’m not worried at all,” added Federer, who will face compatriot Stanislas Wawrinka for a quarter-final berth.
Wawrinka ended the challenge of Australian veteran Lleyton Hewitt 6-4, 7-5.
While Federer downplayed his back trouble, Leonardo Mayer’s back injury was bad enough to have the Argentine pulling out of his scheduled third-round match against Rafael Nadal, sending the fifth-seeded Spaniard into the round of 16 by a walkover.
That meant Nadal had a chance to rest his troublesome left knee, but cost him more of the match experience he says he needs as he continues his comeback from a seven-month injury layoff.
The former World No 1, currently ranked fifth, returned in February, reaching one final and winning two titles in three clay-court tournaments.
This is his first hard-court tournament since injury forced him out of the Miami Masters last March. Nadal remained on course for a possible quarter-final showdown with Federer. But first he faces a potentially tough fourth-round clash with red-hot Latvian Ernests Gulbis, who defeated 20th-seeded Italian Andreas Seppi 5-7, 6-3, 6-4.
>> Tomas Berdych (6) bt Florian Mayer (27) 6-4, 6-1
>> Angelique Kerber (4) bt Yanina Wickmayer 6-1, 7-6 (7/4)
>> Nadia Petrova (10) bt Julia Goerges 6-1, 6-2
>> Samantha Stosur (7) bt Peng Shuai 6-3, 3-6, 6-2
>> Caroline Wozniacki (8) bt Elena Vesnina 6-2, 6-1
>> Mona Barthel bt Ana Ivanovic (11) 6-1, 3-6, 6-0
>> Victoria Azarenka (1) bt Kirsten Flipkens 3-6, 6-3, 6-0