Thiem, a 2019 winner at the tournament in his home country, prevailed 6-4 6-2 in Kitzbuhel.
He will next face compatriot Sebastian Ofner as he seeks a first title since his grand slam breakthrough at the US Open in 2020.
Ofner came from a set down to beat former world number seven Richard Gasquet 1-6 7-5 7-5.
Meanwhile, seventh seed Pedro Martinez saved six out of six break points en route to a 7-6 6-3 victory over Chilean Nicolas Jarry.
At the Croatia Open in Umag, Bernabe Zapata Miralles set up a round of 16 meeting with third seed Holger Rune by beating Croatian Dino Prizmic, who retired when facing a 6-4 3-0 deficit.
Alex Molcan is safely through to the next round after defeating Duje Ajdukovic, while French 23-year-old Corentin Moutet cruised to a straight-sets victory over sixth seed Daniel Altmaier.
Thiem, last in action in an Australian Open final loss to Novak Djokovic, returned with a 6-2 4-6 6-1 victory over wildcard Felipe Meligeni Alves on Tuesday.
The 2017 champion of the ATP 500 event played on clay in Brazil, top seed Thiem grabbed two breaks of serve in the deciding set.
Having started 2020 with four losses in five matches, Borna Coric found a victory by overcoming Juan Ignacio Londero 7-6 (7-5) 7-5.
Dusan Lajovic joined Thiem and Coric as the three seeds to win, but two fell in the opening round.
Casper Ruud, coming off a title win at the Argentina Open, went down to qualifier Gianluca Mager 7-6 (7-4) 7-5.
Guido Pella, the 2016 runner-up, was edged by Thiago Monteiro 5-7 6-4 7-6 (7-3) after just over three hours.
At the Delray Beach Open, Sock claimed his first non-Laver Cup singles win since late 2018.
The American 2017 champion, a wildcard, battled past last year's winner Radu Albot 3-6 6-3 7-6 (7-2), saving a match point in the final set and breaking down in tears following his victory.
Canadian second seed Milos Raonic brushed past lucky loser Denis Istomin 6-2 6-2 and Reilly Opelka served 20 aces in a 6-7 (5-7) 6-4 7-6 (7-4) victory over Ernests Gulbis.
Ugo Humbert, the French sixth seed, battled through, while third seed Taylor Fritz fell to qualifier Cameron Norrie 6-4 6-7 (4-7) 6-4.
The American had lost to Corentin Moutet on the clay in Italy but was back to form in Antwerp in only his second meeting with the Serbian.
Lajovic won their previous encounter at Indian Wells in 2017 but Tiafoe saved two set points in the second set to prevail 6-3 7-6 (8-6) and progress to the second round.
Tiafoe was not the only player to knock out a seed on the ATP Tour on Monday, as his compatriot Steve Johnson claimed victory over Marin Cilic at the Cologne Championships.
Johnson spurned four set points as the opener was sent to a tie-break. However, he prevailed in the shoot-out and then broke the ninth seed to love in the first game of the second.
Cilic never threatened to break back as the 2014 US Open champion slipped to a surprise defeat.
Fognini, competing for the first time since undergoing arthroscopic surgery on both ankles in May, went down 6-1 6-2 to world 303 Huesler in a little under an hour.
The 2011 French Open quarter-finalist was broken in the second game and Huesler, who had just two previous career wins on the ATP Tour, broke again in the sixth.
After saving three break points in the early stages of the third set, Huesler held serve and secured a famous win in Kitzbuhel with minimal fuss.
Feliciano Lopez awaits in the last eight after battling to a 7-5 6-7 (4-7) 7-6 (7-3) victory over seventh seed Guido Pella in three hours.
World number 84 Ruusuvuori saved a set point in the first-set tie-break on his way to a 7-6 (8-6) 6-4 victory and will now face Ilya Ivashka for a place in the semi-finals.
There was nearly another upset as home hopeful Alexander Bublik, seeded second, had to recover from a set down to overcome Miomir Kecmanovic 2-6 6-3 7-5.
Carlos Taberner awaits Bublik in the next round after the Spaniard beat Egor Gerasimov 5-7 7-6(5) 7-5.
Kwon Soon-woo and James Duckworth saw off Dusan Lajovic and Filip Krajinovic respectively in straight sets to remain a course for glory.
At the Moselle Open in Metz, meanwhile, Gael Monfils took out Philipp Kohlschreiber 7-6(2) 6-4 to reach the quarter-finals on home soil.
Tournament favourite Hubert Hurkacz made light work of 2016 champion Lucas Pouille with a 6-2 6-3 victory to set up a meeting with Andy Murray in the quarter-finals.
Elsewhere on Thursday, German qualifier Peter Gojowczyk proved too strong for Karen Khachanov and will now face Marcos Giron, who upset fourth seed Alex de Minaur.
World number two and top overall seed Alcaraz was strong in his 6-4 7-6 (7-0) victory over Serbia's Dusan Lajovic, improving his unbeaten record in 2023 to 6-0.
Alcaraz has his eyes set on his second title win in a row after also emerging triumphant in last week's Argentina Open.
Meanwhile, Norrie had to fight back from an early deficit to eliminate Hugo Delien 4-6 6-1 6-4, with the world number 13 and second seed now boasting eight wins from his past nine matches. The only loss during that stretch was to Alcaraz in the Argentina Open decider.
For a chance to avenge that loss, Norrie will have to beat Bernabe Zapata Miralles after he overcame Albert Ramos-Vinolas 6-4 2-6 6-4 in an all-Spanish quarter-final.
Alcaraz will contend with Nicolas Jarry, after the unseeded Chilean knocked out his second seeded opponent of the tournament, this time getting the better of Sebastian Baez 6-3 7-6 (7-3).
The 22-year-old Greek did not have it all his own way in the 7-6 (7-5) 6-2 win, but after coming out on top in a tricky first set, he maintained his level and saw off Lajovic.
Tsitsipas had been in good form during wins over Dan Evans and Pablo Cuevas in the previous two rounds, not dropping a set in the process, though world number 24 Lajovic looked likely to pose more of a threat.
And the Serbian appeared poised to take the first set when going 5-3 up in the tiebreaker, only for Tsitsipas to rattle off four points in succession and take the lead.
Although there were then three straight breaks of serve to start the second set, it was mostly plain sailing from then on for world number five Tsitsipas, who once again relished the setting, with up to 2,300 fans permitted to attend the tournament despite the ongoing coronavirus crisis.
"It was a perfect day, sunny, good people, good atmosphere and good clay," Tsitsipas said in his on-court interview. "Dusan is a difficult opponent to play on clay, with a lot of spin and variation in his shots. I think I had to do something extra for the victory today. I will keep working hard."
Up next for the 2019 Australian Open semi-finalist is Chile's Cristian Garin, who impressively fought back from a set down to beat Alexander Bublik 3-6 6-4 6-4 to reach a third semi-final – all on clay – this year.
The other last-four clash will see the in-form Casper Ruud – 7-5 3-6 6-1 winner over Ugo Humbert – face Andrey Rublev, who impressed with his aggression in a 6-2 7-5 defeat of Roberto Bautista Agut.
The ATP 500 clay-court competition was given special permission by local authorities to allow up to 2,300 people to attend on each day, with the tournament originally postponed in July due to the coronavirus pandemic.
And Tsitsipas relished having fans in attendance, which, along with playing against someone he idolised as a youngster, created the conditions that caused him to lose focus for a little while.
"I have a lot of respect for him. He is a very difficult opponent to face, particularly on this surface," Tsitsipas, 22, said of his 34-year-old opponent. "He is a good friend and one of my idols growing up. It was a great match and I enjoyed it.
"There was a certain point in the match when I forgot I needed to win, as I was enjoying the game and the atmosphere, the crowd. I was playing with positive vibes and energy."
Tsitsipas will now meet Dusan Lajovic, who swept aside Karen Khachanov in emphatic fashion, winning 6-1 6-2 in just over an hour.
Casper Ruud was similarly impressive as he saw off Fabio Fognini 6-3 6-3, and he will meet Ugo Humbert – the Frenchman having eliminated Jiri Vesely 6-4 6-3.
