The Commodores (25-10) had a first-round 13-0 run for a healthy lead they enjoyed the bulk of the second half.
Harvard, seeded 12th, made things interesting, however, getting within 70-65 with 1:51 to go. But Jeffrey Taylor made a pair of free throws for Vanderbilt and Jenkins went 6-for-6 from the line over the final minute in clinching the win.
Vanderbilt, the No. 5 seed, heads into Saturday's third round against fourth-seeded Wisconsin. The Badgers (25-9) were 73-49 winners over Montana in their second-round game.
Jenkins ended up 10-of-13 from the free-throw line and also made 7-of-12 field-goal attempts. Brad Tinsley added 16 points and Taylor 15 for the Commodores.
Harvard (26-5) was led by Laurent Rivard with 20 points. Rivard was 6-of-7 from 3-point range. Kyle Casey had 13 points and Brandyn Curry 12 for the Crimson.