Left out of the national title game, Colt McCoy and Texas made the most of their trip to the Fiesta Bowl.

McCoy hit Quan Cosby for a 26-yard touchdown with 16 seconds to play, lifting third-ranked Texas to a 24-21 victory over No. 10 Ohio State on Monday night.

The Longhorns had hoped to use the Fiesta Bowl to persuade voters they deserved a share of the national championship if Oklahoma beats Florida in Thursday night’s BCS final. The Associated Press Top 25 is Texas’ only chance at nabbing a slice of the title but the close victory over the Buckeyes may not be enough to persuade voters.

‘‘I don’t think there’s anybody in the country who can beat us at this point,’’ McCoy said.

The Buckeyes nearly pulled off the upset behind quarterbacks Terrelle Pryor and Todd Boeckman but instead went down to a third straight BCS bowl loss.

McCoy, the Heisman Trophy runner-up, calmly led the Longhorns 78 yards in 11 plays and 1:42 without calling a timeout. On the touchdown, Cosby caught a short pass, slipped a tackle and sprinted toward the goal line before diving into the end zone.

The Longhorns (12-1) rebounded after Ohio State (10-3) had taken a 21-17 lead on a 15-yard run by Dan Herron with 2:05 to go.

That score came five minutes after Boeckman hit Pryor for a 5-yard score to cut Texas’ lead to 17-15. Pryor’s pass on the 2-point conversion was incomplete.

For most of the night, the Buckeyes stifled the high-powered Longhorns, who averaged 43.9 points this season but mustered only a field goal in the first half. They didn’t lead until a nifty third-quarter touchdown run by McCoy, who also threw for 414 yards and two scores with an interception.

The Longhorns finished in a three-way tie atop the rugged Big 12 South and thought their 10-point victory over Oklahoma should have put them in the conference title game. But Oklahoma was declared the division winner on a BCS standings tiebreaker, and the Sooners ripped Missouri in the Big 12 playoff to earn a trip to the national championship.

‘‘This team started this way and finished this way, and they’re obviously one of the best teams in the country if not the best,’’ Texas coach Mack Brown said.

The loss was Ohio State’s third straight in a BCS bowl, and capped a 1-6 bowl season for the Big Ten.

‘‘You saw a great football game out there, two teams going at it extremely hard,’’ Ohio State coach Jim Tressel said.

Texas players rushed onto the field after Boeckman’s last-gasp pass hit the turf deep in Texas territory, then gathered in front of the band and sang ‘‘The Eyes of Texas with jubilant fans.

But early on, it looked as if the Buckeyes would finally be celebrating.

Texas brought Bevo, its steer mascot, but left its offense back in Austin, at least in a sluggish first half.

The Longhorns failed to score in the first quarter. Texas was shut out in only four quarters all season — and only once in the first quarter, in a 39-33 loss at Texas Tech on Nov. 1.

The Buckeyes took a 3-0 lead on a 51-yard field goal by Aaron Pettrey midway through the first period. Ohio State drove 43 yards in nine plays, the biggest chunk coming on a 22-yard burst by Chris ‘‘Beanie’’ Wells.

Four minutes into the second quarter, Texas tied it at on a 27-yard field goal by Hunter Lawrence. The Longhorns covered 57 yards, running twice for a total of no yards on the drive.

The Buckeyes responded with a 67-yard march to the Texas 7-yard line. But Buckeyes tackle Bryant Browning was flagged for a false start on third-and-2 at the 7, and after an incomplete pass the Buckeyes had to settle for a 30-yard field goal by Ryan Pretorius to take a 6-3 lead.

Texas’ best chance came late in the half, when McCoy smartly marched the Longhorns from their own 9 to the Ohio State 16 in 47 seconds.

But on third-and-2 at the Buckeyes 16 and 9 seconds to go, McCoy threw perhaps his worst pass of the season. McCoy lobbed the ball toward Cosby at the goal line, but safety Anderson Russell picked it off to kill the threat.

Had McCoy thrown the ball into the seats, the Longhorns would have had time for a chip-shot tying field goal. But they went into the dressing room still down by three.

It didn’t take McCoy long to atone.

No. 3 TEXAS 24, No. 10 OHIO STATE 21

Ohio State 3 3 0 15 — 21

Texas 0 3 14 7 — 24

First Quarter

OSU—FG Pettrey 51, 7:28.

Second Quarter

Tex—FG Lawrence 27, 11:45.

OSU—FG Pretorius 30, 5:39.

Third Quarter

Tex—McCoy 14 run (Lawrence kick), 8:29.

Tex—Cosby 7 pass from McCoy (Lawrence kick), 1:04.

Fourth Quarter

OSU—FG Pettrey 44, 13:22.

OSU—Pryor 5 pass from Boeckman (pass failed), 7:26.

OSU—Herron 15 run (pass failed), 2:05.

Tex—Cosby 26 pass from McCoy (Lawrence kick), :16.

A—72,047.

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OSU Tex

First downs 21 33

Rushes-yards 39-203 28-72

Passing 176 414

Comp-Att-Int 10-25-0 41-59-1

Return Yards 16 0

Punts-Avg. 4-40.3 5-46.8

Fumbles-Lost 1-0 2-0

Penalties-Yards 7-67 8-83

Time of Possession 30:13 29:47

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INDIVIDUAL STATISTICS

RUSHING—Ohio St., C.Wells 16-106, Pryor 15-78, Herron 5-30, M.Wells 1-(minus 2), Boeckman 2-(minus 9). Texas, Ogbonnaya 11-42, Whittaker 6-23, McCoy 7-3, Bobino 1-2, C.Johnson 3-2.

PASSING—Ohio St., Pryor 5-14-0-66, Boeckman 5-11-0-110. Texas, McCoy 41-59-1-414.

RECEIVING—Ohio St., Robiskie 5-116, Posey 2-13, Ballard 1-21, C.Wells 1-21, Pryor 1-5. Texas, Cosby 14-171, Shipley 10-78, Collins 7-60, Kirkendoll 5-41, Ogbonnaya 4-56, Ullman 1-8.