The 30-year-old German, who won the grass-court tournament in 2011, struck nine aces and converted both his break point chances to win in 1 hour, nine minutes.
Kohlschreiber will next face French qualifier Pierre-Hugues Herbert, who upset eighth-seeded Jerzy Janowicz of Poland 7-6 (5), 6-2.
Also Monday, German wild card Dustin Brown beat Russia's Andrey Kuznetsov 6-3, 6-4 to set up a second round meeting with French Open champion Rafael Nadal.
Another German wild card, Peter Gojowczyk, defeated Poland's Michal Przysiezny 7-5, 6-4 for a meeting with third-seeded Milos Raonic of Canada.
Portugal's Joao Sousa beat Germany's Jan-Lennard Struff, another wild card, 6-4, 6-3 and next faces six-time champion Roger Federer, who is seeded second behind Nadal.
Tommy Haas, who won the tournament in 2012, withdrew due to a right shoulder injury.