The Blue Jays improve to 3-2 on the year.
"This team is capable of so much," said Westminster Head Coach Wendy Sanchez. "It's very exciting to see us finally putting those pieces together in a complete team effort."
Westminster also set a gameday record for goals in a game with 12, which hasn't happened since the 2000 season, when it the Blue Jays scored 12 goals twice, also against Stephens.
Schulte and Koonce tie a gameday record held by five Blue Jays, most recently by Paige Townsend who scored four goals last season against Principia.
Schulte and Koonce combined for the first six goals of the game, including Schulte's fourth goal with 20 seconds left in the first half.
Kate Ponder became the third Westminster player to score to open up the second half and make the score 7-0.
Westminster totaled 32 shots in the match.
"Tonight was really important for us because we were able to find success while also getting everyone significant action and working on some new things in preparation for conference play," said Sanchez.
The Blue Jays travel to Cornell College in Iowa Sunday, September 23 to continue nonconference play.