Utah State's next possession ended when Shane Rector misfired on a jumper. Webb made one of two free throws to make it 69-67 before the Aggies missed two chances to tie or regain the lead.
With 43 seconds remaining, Lew Evans was fouled but missed the front end of a 1-and-1.
Utah State got the defense stop it needed, however, when Boise failed to get off a shot with 14 seconds left. But Rector missed and Jackson sealed the deal with a free throw with one second remaining.
"Toughest loss of the year," said coach Tim Duryea.