The Bluejays (7-4, 1-0) erased an 11-point deficit with an 18-4 run over the final 4:21. The third-largest home crowd in school history -- 15,684 -- watched the game at Qwest Center Omaha.
The Bears (11-2, 1-1) trailed by 10 early in the second half before Blake Ahearn hit a baseline jumper that started a 16-0 run. He scored eight of his team's first 10 points during the rally and finished with 21 points.
Missouri State led by as many as 11 points, but Creighton battled back to take a 72-71 lead on a three-pointer by Dane Watts with less than a minute to play.
A free throw by Tolliver with 21 seconds to go and a pair of free throws by Funk four seconds later put the Bluejays up 75-71.
Funk finished with 23 points while Tolliver had 20.
Creighton led 44-37 at the break after shooting 65 percent (17 of 26) from the field in the first half.
The Bluejays used a 10-0 run to take an early nine-point lead, and hit 15 of their 21 shots in the first 15 minutes.
After falling behind 33-22 in the first half, the Bears scored 11 of the next 14 points to pull within three. But Creighton scored six of the last eight points of the half.