After losing senior quarterback Zach Mettenberger in the final game of the season to a torn ACL, the Tigers (10-3) were forced to rely heavily on Hill and a defensive unit that forced three turnovers (two interceptions, one fumble).
Hill was named the game's MVP.
Freshman quarterback Anthony Jennings struggled in his first career start, completing just 7-of-19 passes for 82 yards with an interception while also rushing for a score.
With the victory, LSU set a school record with its fourth straight season with at least 10 wins.
Jake Rudock started the game under center for the Hawkeyes (8-5), but left the game in the second half with an apparent leg injury. He was 9-for-22 passing for 102 yards and an interception before exiting.
C.J. Beathard replaced Rudock and threw for 55 yards and a score on 4-of-7 passing, and Mark Weisman rushed for a score for Iowa, which had won three straight entering the contest.
Jennings got the Tigers on the board just over four minutes in without attempting a pass. Hill rushed for 60 yards on five carries on the drive, including a 42-yard scamper on the game's first play from scrimmage.
After Kenny Hilliard was stopped on the Iowa 2-yard line, Jennings followed his blockers into the end zone for a 7-0 lead.
Hill's first score came at the 7:23 mark of the second. Iowa had forced an LSU punt, but Kevonte Martin-Manley muffed the pint at the Hawkeyes' 39. After Hill picked up a first down on 3rd-and-short inside the Iowa 20, he ran it in from 14 yards out, bouncing off tacklers before carrying a pair of defenders across the goal line.
Iowa finally got on the board with just under six minutes left in the third quarter. John Lowdermilk picked off Jennings and returned for what appeared to be a pick-six. Lowdermilk, though, dropped the ball before crossing the goal line and the Hawkeyes took over on the 1-yard line. On 3rd-and-goal, Weisman ran it in for make it 14-7.
Late in the fourth, Hill capped off his impressive performance with a highlight-reel 37-yard touchdown run. Hill got things started on the drive with runs of 28 and 20 yards on consecutive plays before coming out for a breather. On 3rd-and-5, Hill burst through the line of scrimmage and bounced off Iowa players before breaking free for the score.
Jordan Cotton returned the ensuing kickoff 96 yards to the LSU 4-yard line, and two plays later Beathard found Martin-Manley for the score.
The Hawkeyes were unable to recover the onside kick, but almost got the ball back at midfield with eight seconds left.
LSU had lined up in the victory formation on fourth down and time winding down before a Tigers' player called a timeout to prevent LSU from turning it over on downs at midfield.
Jamie Keehn then punted it out of the timeout, and after several laterals, Christian Kirksey was taken down at the 24 to seal the win.
Hill tied an LSU record with his seventh 100-yard rushing game this season ... LSU star defensive tackle Ego Furgeson was not with team because of a "medical issue" ... LSU has appeared in 14 straight bow games ... The Tigers are 41-2 under Les Miles in games against non-conference opponents since 2005 ... LSU improved to 23-21-1 all-time in bowl games ... The only previous meeting between the teams came in the Citrus Bowl on Jan. 1, 2005, when Iowa came away with a 30-25 victory ... Iowa has appeared in a bowl game in 11 of the past 13 years ... The Hawkeyes are 14-12-1 all-time in bowl games.