Gotcher was 7 of 10 from the field and made 6 of 8 3-pointers. Justin Gray added a season-high 15 points for Texas Tech (6-1).
Entering the game, UT Martin coach Heath Schroyer said his team's game plan was to try and force Texas Tech to shoot from the perimeter and keep the ball out of the paint.
''(Zach) Smith makes them really hard to guard, especially when he can step out and make perimeter shots,'' Schroyer said. ''Gray is a heck of a player. He was really impressive to me.''
Gotcher hit four 3-pointers to help the Red Raiders jump out to a 20-9 lead midway through the first half. ''I think it's a real confidence boost when you see that first shot go in,'' Gotcher said.
Following a Lee 3-pointer, Texas Tech closed the first half on a 19-4 run to take a 39-16 halftime lead. Gray scored seven points during the span.
''Texas Tech is really physical on the wings,'' Schroyer said. ''It made it really hard for us to run offense. They did a great job of taking us out of a lot of stuff, especially in the first half.''
Alex Anderson made a 3 to pull the Skyhawks to 50-39 with 10 minutes left. Gray scored four points to spark 14-4 surge and the Red Raiders cruised from there.
With 4:43 left in the first half, Gray converted a 3-point play after being fouled on a hard drive to the basket from the baseline. It was Texas Tech's first free-throw attempt of the game.
''(Gray) shot 5 for 5 and the rest of the team shot (7),'' Texas Tech coach Tubby Smith said of his team's free throws. ''That gives you an idea of how aggressive he is. And his willingness to take coaching. Because that's what we were telling him. `Take the ball to the basket.'
Both stayed sprawled out on the court, but eventually walked off with help from team trainers. Smith and Schroyer said their players were sore, but fine.
UT Martin: The Skyhawks made their first visit to Texas Tech in program history on Wednesday. UT Martin has played four teams from Texas in its Division I era (Lamar, North Texas, TCU and Houston Baptist). Senior Myles Taylor entered the game in the top 10 of seven UT Martin statistical categories, including first in free throws made and fifth in points.
Texas Tech: The Red Raiders are in the midst of an eight-game home stand. Texas Tech next plays on the road Jan. 6 at Iowa State. Texas Tech has not lost since a Nov. 19 meeting with then-ranked No. 16 Utah.
Texas Tech entered the game averaging 74.7 points per game. The Big 12 is the only conference with all of its members averaging 73 or more points per game.
UT Martin plays at Texas-Rio Grande Valley on Friday.
Texas Tech hosts South Dakota State on Dec. 16.