It was the first contest in the 95-game series since the 2012-13 season, when Pacific was a Big West member.
Edon Maxhuni's 3-pointer gave LBSU a 15-point lead early in the second half, but the 49ers didn't hit their next field goal until four-plus minutes later as Pacific went on a 13-0 run to cut it to 49-47. The Tigers took their first lead of the second half on Dorsey's 3-point play with 8:54 remaining.
Dorsey grabbed an offensive rebound with 47 seconds left and made a shot in the lane for a 72-68 lead 30 seconds later. LBSU missed two free throws on its next possession and Anthony Townes sealed it with two foul shots.
Dorsey, who entered sixth in the nation with a 94.7 free-throw percentage, made all 10 of his free throws for Pacific (8-4).
Temidayo Yussuf had 14 points and 10 rebounds and Gonzaga transfer Bryan Alberts added 13 points for LBSU (3-9), which has losses against UCLA, Arizona State, Mississippi State, Oregon State and USC this season.
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Military academy athletes can get waivers to delay service, go pro
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No. 9 Virginia outscored its first two opponents by a combined 45 points despite shooting 16 percent from 3-point distance.