Falls, a junior from Park Ridge, Ill., scored a season-high 23 points while hitting 7 of 10 shots from the floor, including 5 of 7 from 3-point range.
Chris MacGillis added 22 points for Lawrence (14-1, 8-0 MWC), and Chris Braier turned in another double-double with 14 points and 15 rebounds. Dan Evans had a season-high 12 points for the Vikings.
Lawrence went on a 12-2 run in the first half and held a 38-25 lead at the break. The Vikings led by as many as 16 points in the second half before Knox rallied. The Prairie Fire cut the lead to 56-52 on Jason Harper's jumper with 9:44 left but could not get any closer.
Lawrence then went on a 7-0 run to grab a 73-61 lead with 4:04 left to regain command.
Jared Kelly scored 19 points to pace Knox (7-9. 2-8).