COLUMBIA, Mo. -- Allen Webb's only play of the first half was an errant pitch that gave the ball back to Missouri one play after a Tigers' turnover.

The backup quarterback didn't squander his next opportunity.

Webb ignited a stagnant offense in the second half with two touchdown passes to help his team rally from an early 21-point deficit for a 35-24 victory Saturday.

Kansas State (4-5, 2-4 Big 12) scored 21 points in the fourth quarter against the Big 12's best defense to win its 12th straight against the Tigers (4-5, 2-4).

Antoine Polite's 20-yard touchdown catch from Webb with 9:39 to go put Kansas State ahead for good at 28-24. Three plays later, Brandon Archer intercepted Brad Smith's tipped pass and returned it 25 yards for an 11-point cushion.

Darren Sproles got the first two scores of the comeback on runs of 18 and 74 yards for Kansas State (4-5, 2-4 Big 12). After being held to 30 yards in the first half, he finished with 160 yards on 20 carries.

The Wildcats still need victories in their final two games to become bowl eligible for a 12th straight year.

Smith threw two touchdown passes to Sean Coffey for Missouri, which has lost four in a row and blew its third double-digit lead of the season. The Tigers led Troy 14-0 and Oklahoma State 17-0 before losing.

"I've been doing this for a long time," Tigers coach Gary Pinkel said. "My disappointment is beyond description."

Missouri also has to win its last two games to be eligible for a second straight bowl.

"We've got too much talent to be an average team," Thomson Omboga said. "We're way better than 4-5."

Webb stepped in after Meier was 4-for-16 for 37 yards. Webb was 6-for-8 for 111 yards and added 52 yards on 12 carries.

Missouri built a 21-0 second-quarter lead and led 21-7 at halftime despite an error-plagued start. The Tigers lost fumbles on two of their first three possessions, and also had an interception.

Kansas State was limited to 15 yards in the first quarter and didn't have a first down until midway through the second quarter.

Missouri running back Damien Nash didn't start after sitting out last week due a disciplinary suspension, but had 118 yards on 12 carries. That included a 66-yard run that set up Joe Tantarelli's 24-yard field goal for a 24-21 lead with 13:08 left.

Smith set a school career record with 41 touchdown passes, two more than Jeff Handy totaled from 1991 to 1994. He finished 15-of-34 for 205 yards and ran for 58 yards on 14 carries.