The former US Open champion took two hours and 40 minutes to prevail, his 5-7 7-6 (7-3) 6-4 victory setting up a meeting with another former Flushing Meadows winner, Marin Cilic.
“I didn’t start very well. I got a break in the second set and then I got a bit lucky, I was able to break the match,” Thiem said on court after the match.
“The third set was a real grind. I am very grateful to everyone who came tonight. It is very nice to play in Israel.”
In the other match of the day, Roman Sofiulin defeated Hugo Grenier.
At the Sofia Open, Ilya Ivashka, fresh from reaching the round of 16 of the US Open, defeated Mikael Imer 7-6 (10-8) 4-6 7-5.
There were also victories for Kamil Maiczak and Alexander Lazarov.