Badowski scored all of his points from behind the arc, accounting for 7 of the team's 11 3-pointers. Shaquille Johnson added 12 points for the Lancers.
Longwood finished the first half on a 23-7 run and continued to extend the difference, leading by as many as 32 points after the break.
The Lancers grabbed just 18 total rebounds - compared to 29 for Averett - but forced 18 turnovers.
Carter Jones finished with 17 points for Averett. The Cougars shot 50 percent from the field but went 0 for 8 from behind the arc.
The matchup was the last exhibition game for the Cougars, who will face off against Lynchburg College on Tuesday in regular-season play.
Longwood plays James Madison on Wednesday.