Eleven Americans started in the main draw, and the world No. 73-ranked Querrey is the only one still standing.
Top seed and two-time defending champion Steve Johnson was upset by No. 241-ranked qualifier Daniel Galan in the round of 16, and last year's finalist Tennys Sandgren lost to No. 372-ranked Tipsarevic in his opening round.
Querrey, a two-time Houston finalist in Houston, is seeking his first final of 2019, having lost in the New York semifinals in February. His last final appearance was New York last year.
The 31-year-old will face Christian Garin on Saturday after the No. 73-ranked Chilean knocked out qualifier Henri Laaksonen, 6-3, 6-2.