All they have to do now is keep playing this way.
Luck threw two touchdown passes, Mathis broke the Colts' single-season and career records for sacks by forcing a safety in the second half and the Colts rolled past Houston 25-3 in their best overall performance in two months.
"We needed it," coach Chuck Pagano said. "We talked all week about coming back and even though we had clinched the division, we wanted to start building or gaining some momentum."
Houston (2-12) extended its franchise-record losing streak to 12 and fell to 0-12 all-time in Indy.
The timing for the Colts' late-season turnaround couldn't be better.
After losing 42-28 at Cincinnati last week, the Colts (9-5) learned on the bus trip home they had clinched the AFC South title when Denver beat Tennessee.
At the time, it looked as if the Colts would be locked into the No. 4 seed and would have little to play for.
But with Denver (11-3) losing Thursday night, New England (10-4) losing Sunday at Miami, Indy winning and Cincinnati playing Sunday night at Pittsburgh, the door has cracked just a bit -- if the Colts win their final two games.
The problem, from November through Sunday, was that Indy had not played anywhere near well enough to string back-to-back wins together.
Over those previous six games, Indy lost three times by at least two touchdowns and was outscored 114-24 in the first halves.
Things suddenly changed dramatically.
Luck went up-tempo right from the start and used a heavy dose of bubble screens to open things up down the field. It worked well.
He finished 19 of 32 for 180 yards with the two first-half TD passes that gave the Colts a 20-3 halftime lead.
Indy played without two starting offensive linemen, lost replacement starter Joe Reitz with a concussion on the opening series and lost running back Donald Brown with a stinger later in the first half.
"We practice it," Luck said of the decision to go no-huddle early. "We have had some success with two-minute hurry up so it's good to come out and do that."
The defense forced punts and turnovers and got a safety on Mathis' record-breaking sack. Punt returner Griff Whalen even set up a score with a 51-yard return.
But the excitement was muted.
They still settled for three field goals and Luck was picked off in the red zone when he tried to force a ball into coverage.
"We looked like a team that lost 11 in a row playing a good football team," interim coach Wade Phillips said in his first game since Gary Kubiak was fired. "I thought we could compete with them, but we didn't do a good job of that."
Most of Houston's problems were self-inflicted, again.
Case Keenum was 18 of 34 for 168 yards with two interceptions and no touchdowns.
Andre Johnson, who needed five catches for another 100-reception season, caught four balls for 18 yards. Ben Tate rushed 16 times for 72 yards and was fortunate not to lose a fumble. Houston also finished with 14 penalties, 10 in the first half.
"That was bad today," said Keenum, whose fumble was recovered in the end zone by left tackle Duane Brown after Mathis' strip sack. "My teammates deserve better, my coaches deserve better. Our fans deserve better."
Luck opened the game by throwing a 14-yard TD pass to Whalen for Indy's first opening-drive touchdown since Week 3. After Houston's Randy Bullock made a 49-yard field goal, Darius Butler picked off Keenum to set up Adam Vinatieri's 37-yard kick.
Luck made it 17-3 when he faked another receiver screen, then flipped the ball on a shovel pass to Trent Richardson for a 9-yard score. And after Butler's second interception, Vinatieri made a 43-yard field goal and Indy led 20-3.
"We played good football today, kept the mistakes to a minimum and were just able to get after it," Mathis said. "A little bit of stuff here and there we can improve on, but for the most part, good football."
Mathis, the NFL sacks leader, has 16½ this season and 108 in his career. Longtime teammate and close friend Dwight Freeney held the Colts' previous marks, getting 16 in 2004 and 107½ in his career. ... Houston's 12-game losing streak is the city's professional football record. ... The Colts have gone 29 consecutive games without back-to-back losses. ... Hall of Fame running backs Eric Dickerson and Marshall Faulk joined Indy's Ring of Honor at halftime.
Tom Brady has won his appeal against the NFL, with U.S. District Judge Richard M. Berman criticizing commissioner Roger Goodell for dispensing "his own brand of industrial justice."
Tom Brady wasn't even present for Thursday night's preseason finale between the Patriots and Giants at Gillette Stadium, but he was still the story of the night.
In his weekly radio interview, Patriots president Jonathan Kraft said the team feels vindicated by a federal court decision to overturn Tom Brady's ban and that the team is "ecstatic" for Brady.
Tim Tebow threw two touchdown passes against the New York Jets, his former team, in a strong effort to make the Philadelphia Eagles' 53-man roster.
A week of tumult and controversy continued for the Washington Redskins, who made an off-field stir related to their ticket policy on Thursday before their final preseason game.
Jason Pierre Paul plans to return to the New York Giants next week and the team will examine his hand and make a determination about when he might be available to play, according to a source.