FORT WORTH, Texas -- TCU didn't leave much to chance against lower-level opponents in coach Gary Patterson's previous 15 seasons.

The Horned Frogs lost a shocker at home to Northwestern (La.) State in 2001, Patterson's first season. Lesson learned, and TCU since then cruised to 9-0 against Football Championship Subdivision (formerly Division I-AA) teams.

But the top FCS teams don't mess around anymore, and South Dakota State was Exhibit A on Saturday night.

The FCS eighth-ranked Jackrabbits brought speed, unexpected pace on offense and a refusal to go away.

That heat kept coming on 13th-ranked TCU, but new quarterback Kenny Hill eventually settled in and led the Horned Frogs to a harrowing 59-41 victory at Amon G. Carter Stadium.

Hill, a junior transfer from Texas A&M, threw for 439 yards and two touchdowns and ran for three more. He was the catalyst as TCU (1-0) pulled away after South Dakota State (0-1) tied the game at 31-31 in the third quarter.

"It's really my fault," Patterson said. "We didn't do a good job handling their shifts. We changed some things around and settled down, and better things happened to us."

After rallying from a 10-point deficit for a 24-24 halftime tie, TCU needed a spark to open the second half. It came when Hill found Jaelen Austin for a 60-yard touchdown pass that produced a 31-24 lead. Hill was nearly intercepted a third time earlier on the drive.

"(Turning the ball over) is something we can improve on and something we will watch on film and get better so we don't make the same mistake next week," said Hill, who completed 33 of 49 passes for 439 yards with two touchdowns and two interceptions. "This has been a year and a half of hard work and prayers for me, and it's all coming to fruition. It's a big deal for me."

South Dakota State drove up the gut of TCU's defense to make it 31-31 on Taryn Christion's 16-yard throw to Dallas Goedert. With about 10 minutes to go in the third, TCU and South Dakota State had nearly 700 combined yards of offense.

"Oh yeah, we felt like that the entire game," said Christion of TCU's early mistakes opening the door for a possible upset. "There was never any doubt in my mind that we could win that game. We had chances the entire game. We just missed something. We couldn't capitalize."

Tailback Kyle Hicks (two rushing TDs) capped another long TCU drive with a 3-yard scoring run for a 38-31 edge. As Hill's rhythm improved, he led another long TCU drive, spreading the ball to several receivers. Hill took it the last 6 yards for 45-31 late in the third.

TCU eventually ran 87 plays; South Dakota State had 65.

"They had really good athletes, and their tempo really got to us, especially late in the game," South Dakota State defensive lineman Kellen Soulek said. "You can't really expect to win a game when you give up 59 points."

Christion (19-for-30, 333 yards, three TDs) kept firing at wideout Jake Wieneke, who hauled in a 34-yard score to end the third quarter to pull the Jackrabbits within 45-38. Wieneke (eight catches, 196 yards, two TDs) all night looked like someone FBS schools missed badly on signing.

The Jackrabbits inched closer with a field goal but still trailed 45-41. South Dakota State (6-for-13 on third down) knocked again after another long strike to Wieneke, but TCU's James McFarland sacked Christion to thwart the drive.

The cushion TCU needed came as Hill's long pass went off Dez White's fingers into the grasp of teammate Taj Williams for a 46-yard touchdown and a 52-41 lead with 8:36 left in the game.

"Kenny managed the game after the two early turnovers, but we have to do a better job of getting in shape up front," Patterson said. "We got tired. We had some holding penalties because we couldn't move our feet."

NOTES: South Dakota State fell to 1-8 against the Big 12, with its only victory coming in 2015 at Kansas. TCU improved to 10-1 against FCS programs during coach Gary Patterson's 15-plus seasons. ... Patterson, TCU's all-time winningest coach, needs six victories to get to 150 for his career. ... TCU racked up 125 yards in penalties on 12 infractions. South Dakota State was flagged just five times. ... The remaking of TCU's offense after the departures of QB Trevone Boykin and WR Josh Doctson to the NFL began taking shape. WR Taj Williams, a transfer, and WR KaVontae Turpin, who moved from running back, combined for 18 catches for 220 yards. The Hill-led TCU offense converted 11 of 15 third downs. ... South Dakota State (461) and TCU (662) had a combined 1,123 yards of total offense. ... TCU DT Aaron Curry, a transfer from Nebraska, had 1 1/2 sacks, 2 1/2 tackles for losses and a forced fumble.