Alston scored the Broncos' first four points in overtime but it was Jessup who gave Boise State (2-2) the lead for good with a 3-pointer. He added a steal and dunk plus two free throws.
Jessup was only 3 of 13 from the floor -- 1 of 9 in regulation -- and his only 3-pointer was just the third for Boise State on 19 attempts. But the Broncos were 19 of 27 at the free-throw line to BYU's 5 of 7.
Boise State's RJ Williams added 18 points on 6-of-6 shooting before fouling out with 1:48 left in regulation, which ended at 58-all after neither team scored in the final 1 1/2 minutes.
Alston, who posted his first career double-double, became the first Bronco ever to score at least 20 points in each of the first four games of a season.
No. 21 Ohio State, Penn State out to stop January skids
Ohio State will hopes its troubles are a thing of the past when the No. 21 Buckeyes face a Penn State team dealing with its own adversity on Saturday in University Park, Pa.
No. 18 Seton Hall puts win streak on line vs. St. John's
Seton Hall's plane ride back to New Jersey this week probably wasn't needed. The Pirates, ranked No. 18, could have floated home after a victory Wednesday at No. 5 Butler.
No. 16 Wichita St. aims to start new streak vs. Houston
No. 16 Wichita State will be coming off its first loss since Nov. 27, a nine-game winning streak snapped, when the Shockers host a Houston team Saturday that has won seven of its last eight games.