Odom finished with 26 points, and Kyle Fuller added 12 points and 10 assists for Vanderbilt (13-8, 5-4 Southeastern Conference). The Commodores snapped a three-game skid to their in-state rival.
Tennessee (14-8, 5-4) came in having won two straight overall and five of the last six in this series. The Volunteers wanted to get the Commodores, with seven healthy scholarship players, into foul trouble. But they didn't get Vanderbilt to pile up enough fouls with only Damian Jones fouling out.
Vanderbilt outshot Tennessee 52.2 percent (24 of 46) to 37.7 percent (23 of 61) with a 34-22 edge in the paint despite being outrebounded 41-26.
The Vols tied it up for the fifth and last time at 53 on a bucket by Jeronne Maymon with 6:35 remaining to cap a 14-3 run. Dai-Jon Parker hit a 3-pointer to put Vandy back ahead. Stokes hit one of two free throws to pull the Vols within 57-54 before Jones reached way back to throw down a one-handed, alley-oop dunk off a pass from James Siakam with 4:16 to go.
Jones then fouled out with 2:36 left.
Tennessee finally ended a 6-minute scoring drought when A.J. Davis scored on a layup with 26.2 seconds left. Richardson also hit a jumper with 16.6 seconds left to pull the Vols within 62-60. But Odom hit the free throws, and Darius Thompson's 3-pointer clanked off the rim at the buzzer.
Tennessee had led wire-to-wire in winning its last two games, and the Vols led in the opening minutes in Memorial Gym with their last at 11-9.
Then Odom put Vanderbilt ahead with his second straight 3-pointer on a long fade-away that beat the shot clock with 13:37 left. Odom hit his first three shots outside the arc and his first six shots for 15 points helping Vanderbilt go up 25-18 with 8:07 remaining.
Stokes went 1 of 5 in the first half, and McRae was 2 of 7. One sequence late in the half summed up their shooting woes. McRae missed a jumper, got the rebound and missed another jumper. Stokes rebounded the ball and tried to go to the basket only to have his shot blocked by Jones.
The Vols couldn't even take set up the final shot of the half. McRae dribbled before throwing the ball in only to have Parker pick off his pass, and Fuller finished off the fast break with a layup that counted on goaltending for a 36-26 halftime lead.