The Austrian recorded his 45th win on the circuit for the third straight year and equalled Rafael Nadal and Alexander Zverev for the most in 2018 with a 7-6 (7-4) 6-4 success over Struff.
Struff had three break points in the second set but was unable to convert any of them as Thiem set up a quarter-final clash with Daniil Medvedev, who beat Mikhail Kukushkin.
Mikhail Youzhny's final ever tournament ended at the last-16 stage as Roberto Bautista Agut knocked out the Russian in his 499th tour-level match.
Youzhny, 36, had already confirmed the St Petersburg Open would be his final competition before bowing out and Agut ended his career with a 7-6 (8-6) 3-6 6-3 victory.
"From the beginning until the end, I was professional," Youzhny said in quotes published on the ATP's website.
"The level of my game in the last match shows that I'm retiring actually at a very good level."
Defending champion Damir Dzumhur also advanced to the quarter-finals, where he will face Stan Wawrinka.
Second seed Stefanos Tsitsipas was eliminated at the Moselle Open as Lithuanian Ricardas Berankis secured a come-from-behind 6-7 (5-7) 7-6 (8-6) 6-3 win.
Seventh seed Filip Krajinovic and Benoit Paire were also ousted but fifth seed Nikoloz Basilashvili came from a set down to win.