Frank Booker added nine points off the bench, and Tyler Neal chipped in eight points and 10 rebounds. Ryan Spangler grabbed 13 rebounds for the Sooners (11-1).
Oklahoma finished shooting 39.6 percent from the field and connected on 16 of 20 from the free throw line.
Jordan Green had 10 points to lead the Aggies (8-3), which saw its two-game winning streak snapped.
Fabyon Harris chipped in nine points, and Kourtney Roberson added seven points and 13 rebounds for Texas A&M, which struggled from the floor, shooting 26.9 percent and hitting just eight percent from behind the arc.
The Aggies hit their first 3-pointer - a Jamal Jones triple with 18 minutes left in the first half - and missed the next 20 attempts before Jones hit a 3-pointer with 25 seconds left.
The Aggies failed to get within five points, with the last time coming with 12:46 remaining in the game on a Harris jumper that cut Oklahoma's lead to 33-28.
The Sooners responded by outscoring Texas A&M 15-6 over the next 5 1/2 minutes to take a 48-34 lead on a Spangler putback with 7:15 remaining. Woodard had five points during the run.
Oklahoma's lead grew more, reaching 19 at 54-35 on back-to-back 3-pointers by Neal and Booker with 5:45 remaining.
The Aggies got no closer than 12 the rest of the way.
Both teams struggled from the floor in the first half, with Oklahoma shooting 39 percent and Texas A&M hitting just 5 of 34 shots for 14.7 percent, including 1 of 12 from behind the arc.
Oklahoma used a 7-0 run to open up a 23-14 lead on a Woodard jumper with 3:37 remaining in the first half. Neither team scored over the final 3:37, combining to miss the last eight shots of the half and four turnovers.
Texas A&M was playing without reserve guard J-Mychal Reese and assistant coach John Reese, who were dealing with an issue within their family, the men's basketball program said Saturday. J-Mychal Reese was averaging seven points a game in 16 minutes a contest.