Samford (1-2) took a 41-30 advantage into the break. Austin Peay took the lead for the first time since early in the game on a Chris Freeman layup that made it 65-63 with 1:37 to go and then again on Chris Horton bucket that made it 67-66 with 22 seconds left.
But Horton missed a free-throw after being fouled by Darius Jones-Gibson, who then got the defensive rebound and sent the ball down court. Christen Cunningham, who led Samford with 14 points and five assists, dished it to Taylor, who sank the game winner.
Brandon Roberts had 11 points and Jones-Gibson finished with 10 for Samford.
Horton led Austin Peay (1-2) with 22 points and 12 rebounds.