Lawrence improves to 15-0 and 9-0 in the conference and is the lone unbeaten team left in men's college basketball.
All-America forward Chris Braier posted game highs in points and rebounds for the Vikings, as he scored 18 and grabbed 14 boards. Ryan Kroeger added 16 points off the bench, and Kyle MacGillis had 13 points and a game-high eight assists for Lawrence.
Blaise Rogers scored 16 points to pace the Scots (5-9, 1-8) and was one of four players in double figures.
Lawrence led by as many as 13 points in the first half, but Monmouth finished the first half with a 14-6 run to trim the Vikings' advantage to 45-40 at the half.
The Vikings led by as many as 10 points early in the second half, but it was a tight ballgame for much of the rest of the contest.
Rogers' three-point play cut Lawrence's lead to 68-65 with 2:16 left, and the score stayed that way until Kroeger hit a pair of free throws with 41 seconds left.
Ben Rosenblatt added another free throw for the Vikings with 34 seconds remaining, but Anthony Beaird nailed a 3-pointer with 28 ticks left to cut the lead to 71-68.
Rosenblatt then drilled two free throws with 24 seconds remaining, and the Vikings snuffed out any hopes of a comeback when Ben Klekamp blocked Beaird's 3-pointer with 10 seconds remaining.
Lawrence is on the road again Saturday when it travels to Grinnell for a 4:00 p.m. contest.