Jordan Tolbert added nine points, 10 rebounds and two blocks for the Red Raiders (7-4). Dejan Kravic had eight points, eight rebounds and two blocks.
It was Tolbert's first double-digit rebounding performance since pulling down 10 rebounds at Oklahoma on Jan. 17, 2012.
Jamie Adams led Florida A&M (4-9) with 22 points and five steals. Reggie Lewis added 10 points for the Rattlers.
The Red Raiders trailed until Trency Jackson's field goal gave them a 20-19 lead with 5:01 left in the first half. That was the only lead change; Texas Tech eventually led 45-28 just over 3 minutes into the second half.
Texas Tech shot 39 percent from the field but made 84 percent from the free-throw line. The Rattlers made 53 percent from the free-throw line.
Texas Tech's 84 percent from the line was its best performance this season and the best best performance by a Red Raider squad in 30 games, dating back to last season.
The Red Raiders open Big 12 Conference play Saturday at TCU at 5 p.m. The game can be seen on FOX Sports Southwest.