Craig Loston's fourth-quarter interception stopped a potential game-tying drive, giving Hill a chance to put the game out of reach by carrying four times for 87 yards on a six-play, 92-yard march that gave LSU (10-3) a 21-7 lead.
Iowa (8-5) pulled within a touchdown after Jordan Cotton returned the ensuing kickoff to the Tigers 4.
Jennings rushed for one touchdown, but the freshman threw for only 82 yards and was intercepted once and sacked four times while standing in for the injured Zach Mettenberger in his first college start.
C.J. Beathard replaced Jake Rudock at quarterback for Iowa on the first play of the fourth quarter. His fourth-down interception stopped one promising drive, but he also tossed a 4-yard TD pass to Kevonte Martin-Manley that trimmed Iowa's deficit to 21-14 with 1:42 remaining.
Safety John Lowdermilk set up Iowa's other TD — Mark Weisman's 2-yard run in the third quarter — with an interception and 71-yard return to the LSU 1.
Officials initially ruled Lowdermilk, who was untouched on the return, scored. But the TD was reversed when a replay review determined the Iowa defender dropped the ball before crossing the goal line.
The victory enabled LSU to finish with at least 10 wins for a school-record fourth consecutive season. The loss ended Iowa's three-game winning streak.
Jennings struggled to hit open receivers and finished 7 of 19 passing. Hill carried 28 times, averaging 7.7 yards per carry. On the clinching drive, he delivered runs of 2, 28, 20 and, finally 37 yards for his second touchdown. He also scored on a 14-yard run in the second quarter.
Iowa was back in a bowl after staying at home with a 4-8 record in 2012. The Hawkeyes' four regular-season losses came to nationally ranked Michigan State, Ohio State, Wisconsin and Northern Illinois, teams that took a combined record of 45-6 into the Rose, Orange, Capital One and Poinsettia bowls.
LSU's first trip to Tampa since 1989, when the Outback was known as the Hall of Fame Bowl, capped another successful season under Les Miles, but one that fell short of expectations for a program accustomed to contending for national titles.
Besides a three-touchdown loss to Alabama, the Tigers dropped three-point decisions to SEC rivals Georgia and Mississippi, while also displaying their potential by being the only team to defeat No. 2 Auburn during the regular season.
Jennings came off the bench in the closing minutes to finish a comeback victory over Arkansas in the regular-season finale, leading a 99-yard game-winning drive that he finished with a 49-yard TD pass to Travin Dural.
Miles expected Jennings to play well, citing poise as one of the 19-year-old's strongest assets. Iowa didn't have much film to study of the young quarterback, but Hawkeyes coach Kirk Ferentz said any newcomer who entered a program such as LSU's and rose to No. 2 on the depth chart as a true freshman figured to have the makings of a star.
And with a talented supporting cast around him, Jennings didn't have to carry the Tigers on his back Wednesday.
Hill and receivers Odell Beckham Jr. and Jarvis Landry combined with Mettenberger this season to make LSU the first team in SEC history to feature a 3,000-yard passer, two 1,000-yard receivers and a 1,000-yard rusher in the same year. And the Tigers didn't stray from the formula that made them one of the league's top offenses.
Hill broke a 42-yard run on his first carry, setting the tone against an Iowa defense that entered yielding just under 121 yards per game rushing and a little more than 303 overall, third in the Big Ten and seventh nationally. Seven plays later, Jennings finished a 77-yard, game-opening drive with his TD run.
An Iowa fumble on a punt led to Hill's 14-yard TD burst that made it 14-0 midway through the second quarter.
But the Hawkeyes were not discouraged, even after Mike Meyer's 35-yard field goal attempt sailed wide right, leaving Iowa down by 14 in the third quarter.
Lowdermilk's first career interception and long return bolstered hope for a comeback. But without Rudock, who was 9 of 22 for 102 yards and one interception before being injured late in the third quarter, the Hawkeyes came up short.