Wayns made the first two baskets of overtime after teammate James Bell made a pair of free throws, and the Wildcdats (2-0) went 8 of 8 from the free-throw line the rest of the way to hold off the Explorers.
Wayns made all 10 of his free throws and Dominic Cheek, who scored 18 points, was 12 of 14 from the foul line.
La Salle led 31-26 at halftime, and took a 61-56 lead with 1:26 left in regulation. Wayns then made a 3-pointer, before fouling a La Salle player. On the inbounds pass Darrun Hilliard stole the ball along the sideline near midcourt and drove for a layup to tie with 59 seconds left.
Cheek scored eight points in overtime.
The Explorers (1-1) were led by Tyreek Duren with 24 points.