Senior forward Kyle MacGillis paced Lawrence (10-0, 4-0 MWC) with 16 points. All-America forward Chris Braier added 14 points and 10 rebounds for the Vikings.
All-America center Josh Hinz paced Beloit (5-5, 1-2) with 16 points and 10 rebounds.
Lawrence trailed by as many as 14 points in the first half before the Vikings went on an 18-4 run to tie the game at 24-24 with 5:44 left in the first half.
The Vikings, who led 33-30 at the half, led by as many as five points and trailed by as much as five in the second half.
The sixth tie of the game was at 58-58 when Hinz drained a 3-pointer with 2:00 left.
MacGillis and Braier sandwiched jumpers around a Beloit turnover to give Lawrence a 62-61 lead with 59 seconds left.
Beloit turned the ball over again and the Bucs were then forced to foul. Senior guard Keven Bradley then hit three free throws in the final 22 seconds to seal the win for the Vikings.
Lawrence returns to action at home on Friday when it entertains Grinnell.