Five other Sooners scored in double figures. Christian James and Jamuni McNeace each scored 14 points, Matt Freeman added 13 points, Brady Manek had 11 points and Jordan Shepherd chipped in with 10 for the Sooners, who took control early and were never seriously threatened.
Zach Jackson led the Mavericks with 24 points and JT Gibson chipped in with 16 for Omaha.
The Sooners (1-0) are a perfect 7-0 in season-openers under Lon Kruger and have won 14 straight overall.
Omaha (0-2) was coming off a season-opening loss to Montana State on Friday.
Oklahoma led by only three at 22-19 with about 11 minutes go in the first half when the Sooners started to impose their will and opened up a double-digit lead.
Young's 3-pointer put the Sooners up 36-24 with a little more than six minutes to go in the half.
Oklahoma took a 52-38 lead into intermission and extended the lead to 17 in the first four minutes of the second half.
Mitchell Hahn trimmed the Omaha deficit to nine at 70-61 with a 3-point jumper.
The Sooners did not wilt and stretched the lead to 15 on a Freeman 3-pointer.
The Sooners' defense was stellar, holding the Mavericks to 43.8 percent from the field. The Sooners made 39 of 70 shots (55.7 percent) and held a huge 46-31 advantage on the boards.
The Sooners also had a huge advantage from the free-throw line, sinking 22 of 27 attempts. The Mavericks made 13 of 17 attempts.