Coker, who carried the ball only 10 times, scored on runs of eight and 87 yards for the Volunteers (8-3, 4-3 SEC).
The Commodores (4-8, 1-7) pulled off a 28-24 upset at Tennessee last season to halt a 22-game series losing streak, but still haven't beaten the Vols at home since 1982.
Ainge completed 21-of-26 passes without an interception for Tennessee in its 12th straight win at Vanderbilt Stadium. Robert Meachem caught seven passes for 95 yards and a touchdown, and Jayson Swain had six catches for 76 yards and a touchdown.
Vanderbilt's Chris Nickson passed for 97 yards with a touchdown and two interceptions and led the Commodores in rushing with 44 yards on 13 carries.