Ward ran for two touchdowns and threw for another, leading Houston past turnover-plagued Florida State 38-24 in the Peach Bowl on Thursday.
Florida State, which won the national championship two years ago, was favored by seven points.
"It means that we'll play against anybody, anywhere," Ward said. "We won't back down from anyone."
Florida State's Sean Maguire, who was carted off the field with a sprained left ankle late in the first quarter, returned but threw four interceptions.
Dalvin Cook was held to 33 yards rushing with a touchdown and a lost fumble. That left the Seminoles with five turnovers -- half their total of 10 in 12 regular-season games.
Houston scored the most points allowed by Florida State this season. "Our turnovers had a lot to do with it," said coach Jimbo Fisher.
The No. 9 Seminoles (10-3), who trailed 21-3 at halftime, tried to rally with two fourth-quarter touchdown passes by Maguire.
Fisher said X-rays showed no structural damage to Maguire's ankle.
Maguire said the injury "limited some stuff, but it was fine."
Ward threw for 238 yards and ran for 67 yards for No. 14 Houston (13-1).
"To be on this stage and do it with everybody watching, this bowl is huge," said Houston running back Kenneth Farrow. "It means a lot for our program."
Linebacker Matthew Adams said the win "puts our name out there with all the other great programs."
Ward, the junior who started at wide receiver early last season before becoming a full-time quarterback, had touchdown runs of 7 and 6 yards. He left the game briefly after taking a hit in the third quarter, and was shaken up again with about 4 minutes remaining.
Ward returned to take the final snaps of the game, raising his arm in celebration before laying on his back, wallowing in the confetti which fell from the Georgia Dome roof. He was named offensive MVP of the game.
"It hasn't hit me yet. It just doesn't seem real," Ward said.
Ward completed 25 of 41 passes with one touchdown and one interception.
Houston's only loss this season, to Connecticut, came when Ward was out with an injury. He kept the Florida State defense off-balance by leading the Cougars' fast-tempo, no-huddle attack.
"We're not going to match player for player with them," said Houston coach Tom Herman. "We're just not. We felt we had to use tempo to our advantage."
Maguire's 65-yard scoring pass to Travis Rudolph cut Houston's lead to 24-17 early in the fourth quarter. Ward answered with a 17-yard touchdown pass to Chance Allen, who was left uncovered as Florida State sent a defensive back on a blitz. Maguire added a scoring pass to Jesus Wilson later in the final quarter.
Maguire was hurt in the first quarter when hit by Adams. Maguire couldn't put pressure on his left leg as he was supported by trainers before leaving the field on a cart.
When Maguire was out, backup J.J. Cosentino completed only 1 of 4 passes for 5 yards. Maguire returned midway through the second quarter with the ankle wrapped.
The Seminoles were without quarterback Everett Golson, the Notre Dame transfer who began the season as the starter but was away from the team for the bowl game for personal reasons.
Maguire's last interception came with 25 seconds remaining. He completed 22 of 44 passes for 392 yards with two touchdowns and four interceptions.
The Cougars won 13 games for the second time in school history, following the 2011 season.
A previous version of this story incorrectly said that Ward was the only player to run and throw for 1,000 yards this season.
AP College Football website: collegefootball.ap.org