The Terps kept their third consecutive clean sheet at home, but had to settle for a point after failing to capitalize on their chances.
The Terps, who host Purdue Thursday, are 2-0-1 at Ludwig Field this season.
The Terps struggled generating offense in their first Big Ten match of the season.
Goalkeeper Liz Beardsley made nine saves, but the Terps lost comfortably in their first Big Ten test of the season.
The Terps have won three straight games ahead of Friday's test against No. 6 Penn State.
Terps coach Meghan Ryan Nemzer often calls on Morales to fill in as an offensive and defensive presence in Maryland’s midfield. Nemzer has repeatedly called Morales her “utility player."
The Terps are unbeaten in their last six games and have won three in a row.
The Terps held an opponent without a shot for the first time since 2014 and logged their most shots in a game since 2015 in the dominant victory.
Ava Morales, who entered in the 30th minute, scored the game-winner against Towson.
Morales' first goal of the year in the 52nd minute was all the Terps needed to break a three-game tie streak.