The 11th seed was not at his sparkling best, dropping his serve against the German, but he swiftly regained command in a 6-4 6-4 win.
In the opening match on centre court, Gael Monfils battled back from a set down to secure victory over Andrey Kuznetsov.
The Frenchman recently returned to the circuit after a knee injury and was forced to overcome a sluggish start as he claimed a 4-6 6-3 6-4 win.
During the opener, Kuznetsov snatched 12 of 14 points to go a set up, but lost his grip on the match after surrendering two breaks in the second set.
Serving for the match at 5-4, Monfils hit two big serves to fend off break points and closed out the match.
The highly-rated young Austrian Dominic Thiem suffered a 6-4 6-4 defeat against Lucas Pouille, who will next face eight-time champion Rafael Nadal.