Eric Hayes scored 13, and Landon Milbourne and David Neal each had 12 for the Terrapins (5-2), who improved to 7-3 overall and 5-0 at home in the annual matchup between teams from the Atlantic Coast Conference and Big Ten.
Vasquez helped Maryland finish with a 43-26 rebounding advantage.
Manny Harris led Michigan (5-2) with 15 points, and Zack Novak and DeShawn Sims had 12 apiece.
Down 35-29 at halftime, the Terrapins used 3-pointers by Vasquez and Hayes to quickly pull even. After Harris connected from beyond the arc, Maryland got points from four different players in a 10-0 run that made it 45-38.
"We played a hard-fought game except for the first four minutes of the second half," Sims said.
Maryland led 63-61 when Milbourne blocked a shot by Sims. Vasquez got the loose ball, drove the lane and flipped a no-look pass to Milbourne, who slammed in a dunk that electrified the crowd.
Michigan quickly called a timeout, then missed a shot. The Terrapins got the rebound, and Neal drilled a 3-pointer from the left corner for a 7-point lead with 2:55 left.
Maryland maintained the lead by going 7 of 8 at the free-throw line down the stretch.
The Terps were seeking to bounce back from a 75-48 loss to Georgetown, and did so with a solid performance against Michigan.
"Mentally, we were beaten up a bit. We took some shots the last couple of days," Williams said.
Starting for the first time this season, Neal scored the game's first basket and later hit a jumper in the lane to put the Terrapins up 12-10.
Michigan then went on a 13-2 run that included dunks by Sims and Jevohn Shepherd and 3-pointers by Kelvin Grady and Novak. After the Terrapins closed to 25-23, Harris made two free throws and a layup to give the Wolverines a six-point cushion.
The second half, however, was decidedly different.
"I told them we were going to win the game ... if we came out and outworked them the first part of the second half," Williams said. "I thought we played with more enthusiasm, more intensity. Our defense was better and then all of a sudden we made shots we were missing in the first half."