Former Snider High School standout Brad Sneary paced the 16th-ranked Cougars (10-4) with 16 points, while Bishop Dwenger High School alum Scott Kohne had his ninth double-double of the season with 12 points and 11 rebounds.
Saint Francis was anemic from long range and connected on just a pair of its 20 three-point attempts.
"It's frustrating," LaCross said. "We're doing what we need to do on defense, but fortunately there is time to get some other thing corrected."
Weber International (7-4) jumped out to an early 20-10 advantage, but Saint Francis whittled that deficit away by halftime and trailed just 29-28 at the break.
The Cougars will will host IU-Kokomo on Dec. 27 at 7 p.m. at the Hutzell Athletic Center.