In another indicator of progress, the Terps' opportunities against Rutgers were more dangerous and came closer to finding the back of the net.
The Terps have been shut out in each of their first three conference matchups and earned just one point in Big Ten play.
The Terps lost their first game at home this season after Christin Baumbick's late tally.
The Terps kept their third consecutive clean sheet at home, but had to settle for a point after failing to capitalize on their chances.
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.
The Terps failed to find the back of the net in their first two games of the season.