Jenkins, the SEC's leading scorer, missed Thursday's win over Louisiana State with a sore left foot. He showed no sign of the injury against the Bulldogs.
Jenkins scored 22 points in the second half, including a three-point play and rare four-point play in the final 2:03.
Jeffery Taylor had 20 points for Vanderbilt (23-9), which will play Florida in Saturday's second SEC semifinal. Alabama will face Kentucky in the first semifinal.
Renardo Sidney had 22 points and Ravern Johnson had 18 for Mississippi State (17-14). Dee Bost had 16.
Sidney's second 3-pointer tied the game at 76 with 2:20 remaining. It was the 14th tie of the game and the sixth of second half.
Led by Jenkins, Vanderbilt outscored the Bulldogs 11-5 the rest of the way.
Mississippi State was denied its fifth straight semifinals appearance and a chance to play in the championship game for the third straight year. The Bulldogs lost in overtime to Kentucky in last year's final after beating Tennessee for the 2009 tournament championship.
Sidney, Mississippi State's massive (6-10, 275) forward and leading rebounder, played only two minutes in the first half after picking up two early fouls. Sidney came out after halftime as if determined to make up for lost time.
All but two of Sidney's points came in the second half.
The Bulldogs adjusted to the unexpected early exit for Sidney and, displaying an uncanny knack for buzzer-beating shots, still led 38-36 at halftime.
Bost banked in a shot before the shot clock expired for a 29-28 lead and added another buzzer-beater at the end of the half to give the Bulldogs the lead.
Vanderbilt opened the second half with a 9-0 run that included a steal and basket by Jenkins, followed by his 3-pointer. The surge gave the Commodores a 45-38 lead, but the Bulldogs recovered quickly to resume the pattern of frequent lead changes.
Click here for the Inside Mississippi State Sports blog with Brad Locke.