Published: Sep 04, 2012 7:06 PM EDT
Updated: Sep 05, 2012 6:32 AM EDT

MANHATTAN, Kan. (AP) - One week after piling up a school-record 35 fourth-quarter points, No. 21 Kansas State is preparing for a rematch of the game where it first earned a reputation for winning late.

Miami is coming to town on Saturday.

Wildcats coach Bill Snyder refuses to give the Hurricanes the distinction of a turning point last season, but linebacker Arthur Brown is much more convinced that a dramatic goal-line stand - and an assist from a video review - changed the entire mentality of the team.

Kansas State wound up winning that game 28-24 in Miami and parlayed the mental toughness that it earned on the road into a 10-win season and a trip to the Cotton Bowl.

"That established who we were as a defense," said Brown, one of the Wildcats' captains. "It really helped build our confidence not only as a defense, but as a team, that we could play with anyone in the country, so I really think that was the defining moment not only for that time, or for that game, but for the whole season."

Along with a narrow win over Eastern Kentucky to start the season, Kansas State's triumph against Miami started a trend. The Wildcats went 8-1 in games that came down to one touchdown or less - the most amassed by a team from the Football Bowl Subdivision in more than a decade.

The last team to come close was Washington, which won seven by that margin in 2000.

Kansas State's late-game success in 2011 stood in stark contrast to the previous year, when the team went 4-5 in games decided by fewer than 10 points.

"When Coach first got here, that was his big thing: 'Finish, finish, finish,'" tight end Travis Tannahill said. "We couldn't finish any games."

It was not as if the Wildcats did not position themselves for success.

In 2010, Kansas State outscored its opponents in the fourth quarter seven times, going 3-4 in such contests. All four of those losses - to Baylor, Syracuse and former Big 12 members Missouri and Colorado - were by 10 points or fewer.

Perhaps that is why Snyder spent so much time during spring drills, fall camp and throughout the season trying to get the message of finishing strong through to his team.

"We got that under control last year," Tannahill said. "I think we proved that."

No doubt: The Wildcats were perfect in eight games last season where they scored at least as many points in the final quarter as their opponent.

Snyder boils the transformation down to two components.

First, Kansas State was simply a better team last season. There was more talent on the two-deep roster, the product of savvy recruiting and tireless work since Snyder's return to the sideline.

Second, the core values such as toughness and perseverance that Snyder built the program upon during the late 1980s and early '90s have the power to yield tangible results, particularly when the game is on the line in the closing minutes.

"Some of those things that deal with hard work and not giving in prove true, because we won seven out of eight games decided in the fourth quarter," Snyder said. "Come-from-behind victories, that takes those values. You do not do that on sheer talent.

"It happens because there is something else there."

That proved evident in last season's game against Miami.

The Wildcats were on the road for the first time, playing a nationally recognized opponent, and had scrapped their way to a four-point lead with the fourth quarter winding to a conclusion.

Miami had the ball with first-and-goal at the 2, and an incomplete pass from quarterback Jacory Harris and two stymied rushing attempts left the Hurricanes with one more shot.

What happened next changed the trajectory of Kansas State's season.

Harris rolled left and headed for the corner of the end zone, and linebacker Tre Walker wrapped an arm around his neck and yanked him backward. Initially, officials ruled that Harris got into the end zone, but a video review showed that his knee was down before the goal line.

The Wildcats ran out the remaining seconds to keep their perfect start intact.

Quarterback Collin Klein said the victory inspired confidence in the team, even though it didn't dwell on it long. And while it's nice to look back on success, he said the Wildcats would prefer that Saturday's game doesn't come down to the final minutes.

"Regardless if it was a negative step or a positive step, you've got to leave it behind you and move forward, because otherwise something good happening in the past could still trip you up in the future," Klein said. "We moved forward last year and we've got to have the same mentality this year."