Lawrence improved to 8-0 on the season and NAIA Division I Vanguard fell to 6-6.
All-America forward Chris Braier led Lawrence with a game-high 19 points and a game-high 13 rebounds.
Horace Wormely paced Vanguard with 16 points.
Bradley had been having a relatively quiet night on the offensive end, until Vanguard took the lead late.
Lawrence, which led by as many as nine points and led 29-23 at the half, built its biggest lead of the game at 35-25 on Braier's layup early in the second half.
The Lions chipped away and took their biggest lead at 53-50 when Wormely connected on three free throws with 6:52 left.
A jumper by Braier trimmed the lead to one and then Bradley hit a 3-pointer to put Lawrence ahead to stay with 5:14 left.
The teams traded baskets and Vanguard cut the lead to three points with 2:03 remaining, but Bradley answered for the Vikings.
Bradley scored on a layup with 1:50 left, and following a jumper by Vanguard's Greg Gusiff, he drilled a 3-pointer with 1:15 remaining to put the Vikings up 63-57.
DeAuonte Johnson scored for Vanguard to trim the lead to 63-59, but Levi Seekins missed a 3-pointer with 10 seconds left. Bradley hit a free throw with three seconds left to complete the scoring.
Lawrence is off until Jan. 7, when it resumes Midwest Conference play at home against Ripon.