Jay Cutler threw for 276 yards and a score while running for 89 more for the Commodores. Jennings ran for just 43 yards, but finished with two scores - the last helping Vanderbilt shake off a blown 11-point, third-quarter lead.
Herdley Harrison added a key 18-yard sack on the Demon Deacons' final drive after Wake Forest had pushed to the Commodores' 30 with less than a minute to play.
Micah Andrews ran for a career-best 254 yards on 34 carries for the Demon Deacons, who appeared ready to shake their late-game troubles from last year and stay unbeaten in home openers under fifth-year coach Jim Grobe.
Both teams had trouble finishing close games last year, combining to lose 11 games by seven or fewer points. But this time, Vanderbilt - which appeared headed for another late disappointment when Benjamin Mauk scored on a 1-yard keeper for a 20-17 lead with 10 minutes left - managed to come out ahead at the end.
Trailing by three, the Commodores put together a four-play, 49-yard drive, starting with a 28-yard pass from Cutler to Earl Bennett. Then, after Cutler connected with George Smith for a 7-yard gain, Jennings carried twice for the final 14 yards and a 24-20 lead.
The Demon Deacons tried to answer, getting several clutch throws from Mauk to reach the 30. But on a second-and-10, Harrison beat Wesley Bryant around the left side and ran a retreating Mauk down near midfield with 31 seconds left.
After Mauk threw a third-down incompletion, his final heave to Chris Davis was broken up at the goal line by Josh Allen. Cory Randolph, who split time with Mauk at quarterback before moving to wideout this year, made a diving stab at the deflected ball only to be ruled out of bounds near the 2.
The play stood up after a review, sending the Commodores into sideline celebration.
Andrews was filling in for two-time all-Atlantic Coast Conference running back Chris Barclay, who was suspended for the opener. Wake Forest didn't miss its star rusher, but the Demon Deacons had a series of small breakdowns throughout the game - including a fumble by Mauk inside Vanderbilt's 5 - that proved costly by the time Jennings scored the winner.