After a cold first half, Vanderbilt hit 50 percent (6 of 12) from 3-point range in the second half.
Vanderbilt outrebounded Ole Miss 36-29. Lance Goulbourne added 10 points and 12 rebounds for the Commodores, who will play top-ranked Kentucky on Sunday.
Ole Miss (20-13) briefly took a 32-31 lead early in the second half, but Vanderbilt eventually buried the Rebels with well-timed 3-pointers and relentless defense.
The Rebels were led by Jarvis Summers, who scored 15 points. Ladarius White added 13.
Ole Miss had the pace it wanted from the opening tip - a deliberate, half-court game that kept it close.
The Rebels have been a difficult matchup for teams all season despite having serious deficiencies on the offensive end, making up for it with defense,
Neither team shot well in the first half, but Jenkins hit a pair of late baskets, including a 3-pointer, to push Vanderbilt ahead 25-23.
Ole Miss took a brief 32-31 lead on Holloway's free throw with 16:12 remaining, but it appeared the Rebels simply ran out of their usual boundless energy. They failed to close on shooters like Jenkins, who hit a pair of crucial shots from beyond that arc, including one that put Vanderbilt in front 49-40 with less than nine minutes remaining.
Ole Miss made one last run, pulling within 49-44 with 7:24 remaining, but then it was Tinsley's turn to hit a few big 3-pointers, and Vanderbilt went on an 8-0 run to put the game away.
The Rebels do have some hope for an NCAA tournament at-large bid, though they appear to be a longshot. Kennedy has not been to the tournament in any of his first five seasons and the program hasn't qualified since 2002, which is the longest drought in the SEC.