Martin scored 19 points including three treys while Thomas totaled 16 points and pulled down 11 rebounds. Freshman Angela Beadle scored 13 points and grabbed six rebounds.
Tiffany Clarke led Vandy with 19 points and 10 rebounds. The Commodores earned their victory with 47 percent shooting (31-of-68) and 53 rebounds. Sam Houston was limited to 29 per cent from the floor (19-of-64) with only 39 boards.
Sam Houston (2-1) took an early lead, going up 6-2 on a jumper by Thomas two minutes into the contest. Stephanie Holzer started an 11-0 Vanderbilt run with a layup at the 13:56 mark as the Commodores took the lead to stay.
Jasmine Johnson cut the Vandy lead to four points, 28-24 with 5:40 left in the half. The Commodores led 36-30 at halftime.
The Bearkats cut the margin to three points, 39-36 with 17:40 to play, on a lay-up by Thomas. But Vanderbilt pulled away with an 18-4 run and the Kats could come no closer.
The Sam Houston women will continue their road trip to the South with a contest against Kentucky Friday night in Lexington.