The Rainbow Warriors (2-4, 1-0 Mountain West) amassed 513 yards of total offense to snap a two-game losing streak. The Cowboys (3-3, 1-1) dropped their second straight game.
Wyoming held a 14-0 lead early in the first quarter and a 21-10 edge at halftime, but Hawaii stormed ahead with four second-half scores behind Woolsey, who started the third quarter after starter Taylor Graham left the game with a broken foot on the final play before halftime.
Hawaii's rally started on the last play of the third quarter, when Woolsey released a deep pass just as he was being hit, finding Quinton Pedroza for a 53-yard touchdown.
Four plays later, Trayvon Henderson picked off Wyoming's Colby Kirkegaard with the first of his two interceptions and Woolsey recycled the turnover into a 40-yard scoring strike to Marcus Kemp to give Hawaii its first lead at 31-28.
Diocemy Saint Juste, who rushed for a career-high 135 yards on 17 carries, closed out the scoring with a 16-yard touchdown with 3:32 to play.
Hawaii rushed for 232 yards.
The Warriors entered the game averaging just 19.8 points and 336 yards per game offensively.
Woolsey completed 8 of 9 pass attempts, while Graham was 9-of-17 passing for 108 yards. Pedroza caught a game-high seven passes for 118 yards and two touchdowns.
Linebacker Devyn Harris scored on a 78-yard fumble return in the first quarter.
Henderson, Taz Stevenson and Benneton Fonua had eight tackles apiece for the Rainbow Warriors.
Mark Nzeocha made a game-high 13 tackles for the Cowboys.
In addition to Graham's injury, Hawaii lost running back Steven Lakalaka to a head injury late in the third quarter. He did not return.
It was Hawaii's first win over Wyoming since 1992. The Cowboys had won the last six meetings, including last year's 59-56 overtime win in Laramie.