Tech last won 20 or more games during the 1995-1996 season when they finished 30-2 and went to the Sweet Sixteen.
Saturday's victory also gave coach Bob Knight a 25th season out of 36 years coaching that his teams-Army, Indiana and now Tech-have won at least 20 games.
Will Chavis scored 18 points-12 on 3-pointers-and Kasib Powell added 15 to lead the Raiders.
Tech (20-6, 9-5 Big 12) had one of its best defensive efforts of the season, holding Texas A&M (9-19, 3-11) to just 14 first half points.
Tech took the lead early in the game and held the Aggies scoreless for 10 minutes while scoring 17 points.
"I was pleased at our start in the game," Knight said. "And really liked what I had seen when we got up to a 28-9 lead. I thought we played pretty well at that point and then things kind of evened out."
A&M coach Melvin Watkins said he was disappointed with his team's offensive effort.
"The crowd also had something to do with it," he said. "It was a combination of their physical play, the crowd and our lack of execution that led to the breakdown of on offense."
The Aggies managed to hold Tech scoreless for about six minutes near the end of the first half but were unable to mount an offensive comeback.
Andre Emmett added 13 points for Tech, giving the team four starters in double figures.
Bernard King scored 20 points and Keith Bean added 14 for the Aggies.
The first game between the two teams was much closer, with Tech winning 72-70 in College Station in early January.
Saturday's win gave Tech its first sweep against the Aggies since the 1996-1997 season.
Tech led 35-14 at halftime.
At one point near the end of the first half, Knight stood in front of the scorers' table and urged student to clap instead of chanting "Melvin" after Watkins was slapped with a technical.