The 19-time Grand Slam winner picked up a 6-4 6-4 7-6(4) win to set up a meeting with Richard Gasquet in the last 32 of the competition Down Under.
Struff, yet to pass the second round of a major, performed well but could not live with his second-seed opponent on a day that saw the mercury hit 40°C.
Federer earned a break of serve in the fifth game of the opener, paving the way to get over the line with his third set point.
A single break was all it took in the second set, too, as the Swiss held his own serve to open up a 2-0 advantage in just over an hour.
Despite finally breaking Federer early in the third set, Struff failed to capitalise and a tie-break would be required, which the strong favourite took 7-4 to advance through.