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.
McHargue was 23 of 35 for 236 yards. Jordan Taylor had nine catches for 101 yards and Ross gained 94 yards on 14 carries for the Owls.
After Boswell's first 29-yard field goal closed the halftime gap to 17-13, Crist hit three straight passes for 32 yards and Tony Pierson sprinted 28 yards to set up Taylor Cox's 8-yard touchdown run and give the Jayhawks a 24-13 lead. Pierson had 120 yards rushing for the Jayhawks, while Crist, looking sharper than in his Kansas debut the week before, was 16 of 28 for 144 yards and one TD.
Boswell's second 29-yarder sliced the lead to 24-16 in the final minute of the third quarter.
Kansas' first two scores came off first-quarter turnovers. Greg Brown intercepted McHargue's pass at the Kansas 9 just three plays after the Owls had recovered a kickoff that Kansas muffed on its own 18.
Crist hit four straight passes fueling a 79-yard drive that was aided by a 15-yard Rice penalty but stalled on the 12 when he overthrew a receiver in the end zone on third down. Ron Doherty kicked a 29-yard field goal, making it 3-3 following Boswell's 47-yard field goal earlier.
On the ensuing kickoff, Tyree Williams recovered when Rice's Donte Moore fumbled, and Crist immediately converted the turnover into a 23-yard touchdown pass to Jimmay Mundine for a 10-3 lead.
The Owls responded with an impressive 16-play, 94-yard march capped by Turner Peterson's 1-yard run. On the drive, McHargue hit McDonald and Peterson for gains of 18 and 14 yards on successive plays, then Peterson carried 14 yards to the Kansas 10. Kansas seemed to have stopped the Owls on third down, but defensive holding on Corrigan Powell gave Rice a first-and-goal from the 3.
Pierson gained 41 yards on five carries and Cox bolted up the middle for 21 yards on a 75-yard drive by the Jayhawks that made it 17-10 when Schyler Miles dived into the end zone on third-and-goal from the 1.