World number 57 Millman, who had beaten Federer in four sets in their previous encounter at last year's U.S. Open, put up a strong fight in the opening set but was no match for his opponent at the contest wore on.
Up next for the 20-times Grand Slam champion is Jo-Wilfried Tsonga, who has won the last two matches of their 17 career meetings.
Earlier, world number 14 Borna Coric began his title defence with a 7-6(2) 6-3 victory over Spain's Jaume Munar to move into the second round where he will face Joao Sousa.
David Goffin fired nine aces and won 86% of points on his first serve in a comfortable 6-1 6-1 win over Argentine Guido Pella in 50 minutes. Up next for the Belgian is Radu Albot.
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Wildcard Tsonga defeated fellow Frenchman Benoit Paire 6-4 7-5 but not before the duo delighted the crowd with an impromptu game of foot tennis https://twitter.com/ATP_Tour/status/1140985403299770368 in the second set after Paire's racket slipped from his hand following a serve.
Seventh seed Roberto Bautista Agut overcame Taylor Fritz 7-6(10) 6-0 while local hope Jan-Lennard Struff got past Laslo Djere 6-4 6-4 to set up a meeting with Karen Khachanov.
The Halle Open is a warm-up tournament for Wimbledon which begins on July 1.
(Reporting by Shrivathsa Sridhar in Bengaluru, editing by Pritha Sarkar)
