Thiem, viewed as one of the talents that could, in time, push to enter the tennis elite, finished emphatically with an 135 mph ace, the last of three huge serves with which he closed out.
The 23-year-old reached the semi-finals of the French Open for the second straight year last month, crushing Novak Djokovic in the quarter-finals, and has fourth-round appearances in the Australian Open and U.S. Open.
Although he has yet to replicate that clay and hard-court form on grass, his display against the experienced Simon will leave him confident of getting past American Jared Donaldson or Italian Paolo Lorenzi in the next round.
"It's still not my natural surface," Thiem told Reuters after his win.
"But, of course, these victories give me a lot of confidence, also on this surface. For the first time in the third round of Wimbledon is also pretty special," he added.
What was evident though, as Thiem took control after losing the first set, was that the Austrian has been working on elements of his game that can help him on grass.
"Footwork, of course, is important. Then, of course, I cannot change my swings and everything, but I try to play with less spin, to come in a little bit more. I worked on my volleys," he said.
"I didn't work specifically on my grasscourt game. I think if I improve my game in general, it's also going to improve on grass," he added.
The Austrian now has a 6-2 record against Simon and has won their past five matches although this was their first meeting on grass.
The 32-year-old Simon has shown a liking for the surface in the past -- reaching the Wimbledon quarter-finals in 2015 -- and that showed as he clinched the first set.
But Thiem's serve was strong, he won 78 percent of points on his first serve -- he produced 17 aces overall and hit 45 winners to Simon's 22.
"I felt well at my serve the whole match. I had a quite good percentage, many aces I think. It's an important shot on grass.
"Of course, the last game was perfect for me. I'm happy, especially with my serve today," he added.
(Reporting by Simon Evans, editing by Neil Robinson)
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