Boswell also had kicks of 47, 29 and 29 yards for the Owls (1-1), who got into position for the winning score after Bryce Callahan's interception of Dayne Crist's pass with 3:47 to play.
Rice's Taylor McHargue led a 93-yard drive late in the fourth period that ended when Charles Ross scored from the 2, making it 24-22 at the 4:47 mark. On the two-point conversion attempt, McHargue's pass to Luke Willson was caught out of bounds.
Callahan's second interception of the day put the Owls in business near midfield. On fourth-and-4, McHargue connected with Vance McDonald for 7 yards to the Kansas 40. Three plays later, McHargue ran 12 yards, making sure the strong-legged Boswell was in range to stun the Jayhawks (1-1) with his last-second kick.