Mills scored twice for the Student Princes, who fell to 0-8 overall and 0-3 in the OAC on the season. Her first, almost three minutes into the game, tied the match at 1.
Reed's goal came at the 20:23 mark of the first, which brought HU to with three at 5-2.
Dana Dudley scored her 16th goal of the season a minute later, making it 5-3.
ONU would rattle off 11 goals over the next 20 minutes of play before Mills tallied her second of the game at the 14:45 mark of the second half.
The Polar Bears (2-9, 1-2) were led by Betsy Naugle and Rachel Shipman, who combined for 11 goals.
In goal, Janessa Scott faced a total of 37 shots and made 12 saves.
Heidelberg returns to action on Friday. They visit Wilmington (1-11, 0-5) for a 1 p.m. game.