Abdur-Rahkman, who was fouled by Bruno Fernando, reached the 1,000-point mark of his career with the go-ahead point. The Terrapins had taken the lead with 3.2 seconds remaining on Kevin Huerter's 3-pointer.
Moritz Wagner led the Wolverines (16-4 overall, 5-2 Big Ten) with 18 points and 11 rebounds. Jordan Poole contributed 11 points off the bench and three others, including Abdur-Rahkman, added seven points each.
Michigan has won nine of its last 10 games and was coming off an 82-72 road win over rival Michigan State on Saturday.
Anthony Cowan's 24 points paced Maryland (14-6, 3-4), which has lost three of its last four games. Huerter had 12 points and six rebounds and Darryl Morsell tossed in 10 points.
The Terrapins played without junior guard Dion Wiley, who is recovering from a concussion.
Maryland controlled the first half, leading by as much as 14 points before heading to the locker room with a 30-20 advantage.
Michigan scored the first 10 points of the second half to even the score. That run included a three from Wagner and a three-point play by Zavier Simpson.
Maryland came right back with seven consecutive points but the Wolverines soon took the lead. They went on a 9-0 run that included two Poole 3-pointers for a 45-41 lead.
Later on, Michigan reeled off seven unanswered points to bump it to double digits at 59-49. Charles Matthews' jumper capped it off with 5:50 to go.
The Wolverines went cold for more than three minutes but the Terrapins were only able to shave the deficit in half. Wagner was fouled with 2:48 left and drained the free throws to make it 61-54.
Huerter knocked in a three a minute later to pull Maryland within four points. Cowan's three with 20 seconds left made it a two-point game at 66-64. Simpson then missed two free throws before Huerter's three off a feed from Michal Cekovsky.
The teams match up again on Maryland's home floor Feb. 24.
--Field Level Media
Maryland | Michigan | |
Anthony Cowan 24 | Scoring | Moritz Wagner 18 |
Anthony Cowan 4 | Assists | Charles Matthews 6 |
Kevin Huerter 6 | Rebounds | Moritz Wagner 11 |
Anthony Cowan 4 | Free Throws Made | Muhammad-Ali Abdur-Rahkman 2 |
Bruno Fernando 2 | Steals | Charles Matthews 1 |
Michal Cekovsky 2 | Blocks | Charles Matthews 2 |