Rob Poole gave Siena (4-7) the lead for good on a pair of free throws with 1:47 left and Wright made two more at the 1:04 mark to extend the lead to 68-64.
Bucknell (5-8) twice cut the lead to two and Wright answered each time to get the lead back to four. On the second instance, Siena went over the top on the inbounds play to get Wright an easy layup behind the defense, but Bucknell got within 72-71 on J.C. Show's 3-pointer with 5.7 seconds to go to.
Wright made 1 of 2 free throws with 5.1 seconds, and John Azzinaro missed a 30-footer for Bucknell at the buzzer.
Show, a freshman, set a season-high with 23 points.