The win in Baytown put the Seahawks into second place in NJCAA Region 14's South Zone and squared their season record at 11-11.
Coach Lance Madison's team outrebounded the Runnin' Rebels 46-28 overall and 23-9 in the second half.
Thomas pulled down 13 rebounds and Darrell Jones had 10, giving both a double-double as Lamar State won for the seventh time in the last 10 games.
It was Thomas' fifth double-double of the season. He also had four assists, two steals and a blocked shot. It was the first of the season for Darrell Jones.
"I thought this was one of our better games," Madison said. "We showed some toughness. Our defense has gotten better. We're starting to come together."
After a back-and-forth first half ended with the Seahawks up 40-39, the Rebels took the lead early in the second half. Three straight 3-pointers by the home team had LSCPA down five, 61-56, with 11 minutes left.
But Burney scored five points and Darrell Jones four in a 13-4 run in which the Hawks took the lead for good with 8:15 to play.
The next home game for LSCPA is at 4 p.m. Saturday, Feb. 1 against Jacksonville College.