Competing for the first time since his fourth round defeat by Stefanos Tsitsipas at last month's Australian Open, world number seven Federer overcame a blip midway through his match before rallying to beat Germany's Kohlschreiber.
The 20-times Grand Slam champion, who has been stuck on 99 titles since triumphing at his hometown Basel tournament last October, next faces Fernando Verdasco after the world number 32 got past Italian qualifier Thomas Fabbiano 3-6 6-3 6-2.
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The second-seeded Swiss has never lost to Verdasco in six meetings, last beating the 35-year-old Spanish in Dubai four years ago.
Federer's task in the tournament became a bit easier with seventh seed Milos Raonic and fourth seed Karen Khachanov, both in the same half of the draw as the Swiss, suffering opening round exits.
Russian Khachanov was felled by world number 19 Nikoloz Basilashvili who prevailed 6-4 6-1, while Raonic was beaten 6-4 5-7 6-4 by German Jan-Lennard Struff.
Defending champion Roberto Bautista Agut faces wildcard Ramkumar Ramanathan later on Monday.
Top seed Kei Nishikori is in action on Tuesday with an opening round clash against Frenchman Benoit Paire while third seed Marin Cilic meets Gael Monfils.
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