The Terrapins (2-0) had five players in double-figure scoring for the second straight game.
Along with Cowan, Jared Nickens scored 15 points, Dion Wiley had 13, freshman Darryl Morsell added 12 and Kevin Huerter 10.
The Terrapins shot 61.1 percent (33 of 54) and held a commanding 46-21 lead on the boards. Maryland also drilled 9 of 19 3-point attempts (47.4 percent).
The Hawks (1-1) fell to 0-18 all-time against Maryland. Freshman Cameron Bacote led UMES with 18 points, his second straight double-digit effort. The Hawks shot just 3 of 19 (15.8 percent) behind the arc.
The Terrapins shot 70 percent in the first half (14 of 20) and built a commanding 44-18 lead at the intermission. UMES scored the game's first basket on a driving layup by Bacote, but tthe Terrapins ran off the next 12 points, including two 3-pointers from Wiley off the bench early to start the run.
Maryland ended the first half on a 26-7 blitz as Cowan scored 12 points during that stretch.
The Terrapins, receiving votes in the national polls, face a much sterner test Wednesday, hosting Butler on Nov. 15 as part of the Gavitt Tip-Off Games. The Terrapins have won 28 of their last 30 non-conference home games in three-plus seasons.
UMES, which plays 12 of its first 14 games of the road this season, is at St. Bonaventure on Nov. 15, and won't play at home until Dec. 2.