All-America forward Chris Braier scored 15 points and broke the school's career scoring record. Braier now has 1,555 points, topping the mark of 1,554 set by Joel Dillingham.
Lawrence (25-0) was forced to hold off a furious comeback by St. Thomas (23-6), which trailed by 15 points during the second half.
The Vikings led 54-40 on Braier's layup with 5:21 left, which also was the basket that broke the scoring record.
The Tommies then mounted a serious comeback behind the play of Sean Sweeney, who finished with a game-high 23 points.
Sweeney scored 10 of St. Thomas' next 12 points to trim Lawrence's lead to 56-52 with 2:11 remaining.
After a missed free throw, Isaac Rosefelt scored on a layup to cut the lead to 56-54.
Kyle MacGillis, who finished with 11 points, then hit his only 3-pointer of the game with 41 seconds left to put the Vikings up 59-54. That broke a drought of 4:40 without a field goal for Lawrence.
Sweeney countered with another jumper, but Keven Bradley converted 1 of 2 free throws with 28 seconds left to put Lawrence back up 60-56. Sweeney wasn't done yet as he drilled another long 3-pointer to cut the lead to 60-59 with 20 ticks left.
The Tommies fouled freshman Ryan Kroeger, who knocked down both free throws. Sweeney finally missed from 3-point range, and the Vikings got the ball back with five seconds left when Rosefelt turned it over.
Kroeger was fouled again and hit 1 of 2 free throws to seal the win.
Lawrence advances to face Illinois Wesleyan next Friday at a site to be determined. Illinois Wesleyan won 85-71 at UW-Whitewater on Saturday. The site of next weekend's sectional will be announced no later than Monday.