A runner-up in last year???s tournament, Federer was broken once to drop the opening set and trailed 3-1 in the second against a player ranked 153rd in the world.
However, the Swiss top seed, who had received a first-round bye, broke Millman twice to level the match before putting away two of four break points in the decider to seal a 4-6 6-4 6-3 win in just over two hours.
“I was under a lot of pressure and I thought I got quite lucky in the second set,” said Federer. “He was playing some great tennis until the last couple of games, so credit to him.”
Federer, who needs just three more wins to chalk up 1,000 career victories, looked a shadow of the player who has captured 17 Grand Slam titles when he committed 38 unforced errors at the Pat Rafter Arena.
The world No 2 conceded the opening set when he sprayed a forehand volley over the baseline then fell behind in the second when he dropped serve for the second time in the match.
But once Federer elevated his game and began to eliminate some of his mistakes, Millman, a 25-year-old local from Brisbane, was unable to stay with him.
Federer twice broke Millman’s serve to claim the second set then broke him twice more in the decider to book his place in Friday’s quarter-finals against James Duckworth, another wildcard recipient.
The 33-year-old was unfazed by his rusty start and relieved to begin 2015 with a victory as he prepares for the Australian Open.
“It’s the first match of the season, so you never know what to expect,” he said. “I was sweating like crazy. I was just happy to win.”