A two-time runner-up in Houston, Querrey reached the semi-finals thanks to a hard-fought 7-6 (8-6) 7-6 (7-4) victory against the Serb.
Querrey saved two set points in the opener as before seeing off Tipsarevic to move through to the final four without dropping a set.
"My first two matches were pretty clean, but this match was more about fighting your way through it," said Querrey. "There were some frustrating moments against a tough opponent, but I found a way to win those tie-breaks and that's what tennis is about sometimes."
The American eighth seed will next meet Chilean Christian Garin for a place in the ATP tournament decider.
Garin – who saved five match points in his second-round triumph over second seed Jeremy Chardy – accounted for qualifier Henri Laaksonen 6-3 6-2.
Celebrating his 33rd birthday, former champion Marcel Granollers lost 6-1 6-0 to ruthless Norwegian Casper Ruud.
Daniel Elahi Galan was serving at 6-1 4-6 3-3 when his match against seventh seed Jordan Thompson was suspended and rescheduled for Saturday, with the winner to face Ruud.