Vanderbilt took a 32-29 lead into halftime.
But Michigan opened the second half with a 19-5 run, including seven by freshman point guard Daniel Horton and four each fellow frosh guard Lester Brown and senior forward LaVell Blanchard.
Then Michigan held on to withstand an 11-0 Vandy run late in the game to gain the victory.
LaVell Blanchard led Michigan with 19 points, followed by Daniel Horton with 17 and Lester Abram with 13.
Vanderbilt is now 6-3 on he season.
Mens Hoopsters Beat Vanderbilt
The Michigan Insider Top Stories
Tweet Roundup: Rome scrimmageRounding up the sights and sounds of Michigan's final practice in Rome.
The Michigan Insider1:01 PM
Gary growing into leadership roleThe quiet giant Rashan Gary is working to become more of a vocal leader this season.
The Michigan Insider12:27 PM
Tarik Black has high expectations for himselfTarik Black is hungry to get better.
The Michigan Insider11:51 AM
Chiefs select Jehu Chesson No. 139 overallJehu Chesson is the ninth Wolverine taken in the first four rounds of the draft.
The Michigan Insider10:49 AM