B.J. Cunningham made an acrobatic grab for the go-ahead touchdown with two minutes left. Edwin Baker added a 25-yard scoring run and Eric Gordon intercepted Dan Persa to seal a wild win.
The Spartans face another big hurdle next week when they visit Iowa in a game that could go a long way toward determining the Big Ten champion.
No. 18 Missouri 36, No. 3 Oklahoma 27
At Columbia, Missouri, Jerrell Jackson spun free from a knot of tacklers on a 38-yard reception for the go-ahead score, sparking a 16-point fourth quarter that helped Missouri upend the top team in the BCS standings.
The third-ranked Sooners committed three costly turnovers, out of character considering they had only five giveaways the first six games. Two of the turnovers led to 10 points and the other squelched a drive deep in Missouri territory, and the Sooners also missed a chip-shot field goal.
CBSSports.com: College Football
No. 4 TCU 38, Air Force 7
At Fort Worth, Texas, Ed Wesley had a career-high 209 yards and two touchdowns, and the TCU defense stiffened after giving up its first October touchdown, leading the Horned Frogs to a victory over Air Force.
Wesley had more yards by himself than the nation's No. 1 rushing offense as the Frogs piled up 377 yards on the ground, 30 more than the Falcons averaged coming in.
No. 5 Auburn 24, No. 6 LSU 17
At Auburn, Alabama, Cam Newton ran for 217 yards and Onterio McCalebb sprinted 70 yards for the go-ahead score with 5:05 left to lift Auburn to a victory over LSU.
The host Tigers moved on as the powerful league's last unbeaten team. LSU finally had a Les Miles gamble backfire in an adventurous season.
No. 7 Alabama 41, Tennessee 10
At Knoxville, Tennessee, Trent Richardson's 65-yard touchdown run and 5-yard touchdown reception were part of 28 unanswered second-half points as Alabama beat Tennessee.
Greg McElroy completed 21 of 32 for 264 yards, mostly to Julio Jones, who set an Alabama single-game record with 221 yards on 12 catches.
No. 9 Utah 59, Colorado State 6
At Salt Lake City, Jordan Wynn threw for 321 yards and three touchdowns in drizzly weather and Utah thrashed Colorado State to stay unbeaten.
The sophomore quarterback went 23 of 29 and reached the 300-yard mark for the third time in his career.
No. 10 Wisconsin 31, No. 13 Iowa 30
At Iowa City, Iowa, Montee Ball ran 8 yards for a touchdown with 1:06 left and Wisconsin rallied to beat Iowa.
Scott Tolzien threw for 205 yards and a touchdown, John Clay added a pair of touchdowns for the Badgers, who kept their final drive alive by converting a fake punt deep in their own territory.
No. 11 Ohio State 49, Purdue 0
At Columbus, Ohio, Terrelle Pryor threw for three scores, Dan Herron ran for two and No. 11 Ohio State showed it was over its loss to Wisconsin that cost it the No. 1 ranking with a victory over Purdue, which didn't exceed 100 yards in total offense until its final possession.
No. 12 Stanford 38, Washington State 28
At Stanford, California, Andrew Luck threw for 190 yards and three touchdowns to help Stanford beat Washington State to post its best record after seven games in 40 years.
Stepfan Taylor ran for 142 yards and two touchdowns for the Cardinal, who hadn't won six of seven to open a season since Heisman Trophy winner Jim Plunkett helped them do it in 1970 on the way to the Rose Bowl.
No. 14 Nebraska 51, No. 17 Oklahoma State 41
At Stillwater, Oklahoma, Taylor Martinez set a Nebraska freshman record with 323 yards passing and threw a career-high five touchdown passes as the Cornhuskers knocked Oklahoma State from the ranks of the unbeaten.
Syracuse 19, No. 20 West Virginia 14
At Morgantown, West Virginia, Ryan Nassib threw a touchdown pass, Ross Krautman kicked four field goals and Syracuse scored nine points off turnovers in ending an eight-game losing streak to West Virginia. West Virginia quarterback Geno Smith threw three first-half interceptions and was sacked five times. Neither team scored after halftime.
No. 15 Arizona 44, Washington 14
At Tucson, Arizona, Nic Grigsby and Keola Antolin ran for two touchdowns apiece and Matt Scott had no trouble replacing Nick Foles as Arizona easily handled up-and-down Washington.
No. 19 South Carolina 21, Vanderbilt 7
At Nashville, Tennessee, Brian Maddox rushed for a career-high 146 yards and the game-clinching touchdown to lead South Carolina to a difficult win over Vanderbilt, giving Steve Spurrier his 40th victory with the Gamecocks.
Syracuse 19, No. 20 West Virginia 14
At Morgantown, West Virginia, Ryan Nassib threw a touchdown pass and Ross Krautman kicked four field goals as Syracuse scored nine points off turnovers in shocking West Virginia.
No. 21 Arkansas 38, Mississippi 24
At Fayetteville, Arkansas, Knile Davis ran for 176 yards and three touchdowns, and No. 21 Arkansas waited out two weather delays to beat former coach Houston Nutt and Mississippi.
Iowa State 28, No. 22 Texas 21
At Austin, Texas, Austen Arnaud passed for two touchdowns, Alexander Robinson ran for 120 yards and two scores as Iowa State beat Texas for the first time, and handed the Longhorns a second straight home loss for the first time since 1997.
No. 23 Virginia Tech 44, Duke 7
At Blacksburg, Virginia, Tyrod Taylor threw for 280 yards and three touchdowns and Virginia Tech rolled to a victory over Duke.
No. 24 Mississippi State 29, UAB 24
At Starkville, Mississippi, freshman LaDarius Perkins rushed for 131 yards and a touchdown as Mississippi State survived an upset scare to beat Alabama-Birmingham.
No. 25 Miami 33, North Carolina 10
At Miami, Jacory Harris threw three touchdown passes to move into second place on Miami's career list and Damien Berry ran for his fourth straight game of 100-plus yards and the Hurricanes scored 30 straight points to easily get past North Carolina.