Walsh missed a 42-yard attempt with 7:40 remaining that would have given the Vikings the lead, but they regained the ball with 3:55 to go and marched 71 yards to set up another try.
McLeod Bethel-Thompson directed the drive, during which he was 3-for-3 for 48 yards. He went 19-of-26 overall for 187 yards and hit Joe Banyard with an 11-yard touchdown pass in the second quarter.
Minnesota trailed by three at halftime, but Marcus Sherels returned the third-quarter kickoff 109 yards for a touchdown.
Rusty Smith, trying to capture a spot on the Tennessee roster, completed 13-of-21 passes for 178 yards with a touchdown an interceptions.
Both teams finished the exhibition season at 1-3.
Tennessee will visit Pittsburgh on Sept. 8 to start the regular season. Minnesota will also be on the road that day to take on Detroit.