Matosevic blew a chance to claim the first set but Isner ultimately sealed the tiebreak 8-6.
World number 12 Isner broke Matosevic in the seventh game of the second set and closed the match with a thunderbolt ace.
“I knew he was struggling out there a little bit and he knew I was struggling out there a little bit,” Isner told reporters.
“A lot of times those situations are a big advantage for me because I can muster up enough energy to pop some big serves in.
“The beginning of the second set it felt like someone put us in the oven. It was rough. There's only one option for me there, play big and play aggressive. A lot of times it works out.”
The 21-year-old Jack Sock booked a semi-final with Isner with a 7-6 6-2 win over Slovakia’s Lukas Lacko, assuring the home nation of someone to cheer in the final.
The other semi-final will be fought out between German Benjamin Becker and Israel’s Dudi Sela.
Becker took out Thiemo De Bakker of the Netherlands in straight sets, winning 6-4 6-2 in just over an hour. Sela upset fourth seeded Canadian Vasek Pospisil 7-5 1-6 6-2
(Writing by Ben Everill; Editing by Ian Ransom)
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