The world number seven banged down 12 aces and struck 32 winners in the one-hour and 23-minute contest.
The 27-year-old, a two-time quarter-finalist at Wimbledon, will next face Hungarian Marton Fucsovics at the ATP 250 event. Fucsovics beat France's Arthur Rinderknech 7-6(4), 6-3 to book a place in the quarters.
American third seed Ben Shelton also prevailed against Frenchman Pierre-Hugues Herbert 7-6(4), 7-5 in 50 minutes to move into the quarters.
The 22-year-old world number 12 will next take on Czech eighth seed Jiri Lehecka, who later beat German Jan-Lennard Struff 6-4, 7-5.
"I'm really happy. Happy to get my first win here in Stuttgart," Shelton said.
"I thought I played great in the big moments today down the stretch, and I'm just really happy to be back on the grass competing.
"It's a completely different game, playing on this surface, and hopefully I can get better and better as this week goes."