Davis returned two kickoffs for touchdowns to lead the Texans to a 42-28 win over the Jacksonville Jaguars (11-5), who rested many starters with their playoff spot secure.
Jacksonville will play at Pittsburgh on Saturday night.
"I had a conversation about him, and the conversation was, 'Do we think he's a kick returner?"' Kubiak said. "I can't remember how our conversation ended, but there's no doubt that he's a kick returner."
The victory gave the Texans (8-8) a .500 finish for the first time in their six-year history, and their 42 points were a team record.
"It's kind of bad that it feels this good, but I'll take it," said offensive lineman Chester Pitts, who has started every game in team history. "It's been a long road. I've been through a lot with this team and ... I appreciate every part of it."
Ron Dayne added two touchdowns and 88 yards rushing for Houston in his return after missing two starts with a sore ankle. He set a career-high with 773 yards this season.
"It just felt good to be able to get the win and not be losers anymore," Dayne said.
Davis' two returns came on consecutive kickoffs. He became the first player in the NFL this season to return two for scores in a game and the seventh player in league history to achieve the feat.
He also had a fumble recovery that led to a touchdown.
Davis is an unrestricted free agent.
"I was a little bit worried about where I stood on the team," he said. "I realized that this game is about getting opportunities and making the most of them."
His first return, a 97-yarder, came 15 seconds before halftime and put Houston ahead 21-14. He evaded the first wave of defenders before cutting to the outside, where he tightroped the sideline the rest of the way for the score.
"I think I have that type of sneaky speed where a lot of guys don't think I'm going to run that fast until I get by them," said Davis, a college track standout.
He turned in the longest play in Texans history on the second one. Davis dashed 104 yards on the opening kickoff of the second half to make it 28-14. This time, he got a block from Charlie Anderson and then zigzagged down the middle of the field before breaking away from the pack and racing to the end zone.
The Jaguars started Quinn Gray, who threw four touchdown passes, in place of David Garrard. Six other starters, including running back Fred Taylor and defensive end Paul Spicer, were inactive.
"Bottom line is our approach today was to be smart," coach Jack Del Rio said. "We earned that right. We earned the ability to be able to do that. We hope to be as fresh as possible going forward next week."
Davis is the first player to have two kickoff returns for touchdowns in a game since Chicago's Devin Hester did it Dec. 11, 2006, against St. Louis. Davis now has three kickoff returns for touchdowns this season and four in his career.
Fullback Vonta Leach met him on the Houston sideline after the second one and waved a towel as if he was fanning a flame. Davis walked by, smiling.
Gray was 25-of-39 for 302 yards, while Matt Jones had eight receptions for 138 yards.
"It's not really satisfying," Gray said. "Stats are good for the books and the records, but when it comes to this team we always want to win."
Ernest Wilford's 6-yard touchdown catch less than 30 seconds before halftime briefly tied the game at 14 before Davis had his first score.
The Texans had gone up 14-7 with about 31/2 minutes left in the half on a short fourth-down pass from Sage Rosenfels to a leaping Owen Daniels.
Jacksonville's Chad Owens, recently signed from the practice squad, muffed a punt that was recovered by Davis at the 6-yard line to set up Houston's first score. Dayne's 2-yard touchdown run made it 7-7 early in the second quarter.
Dayne's second score was a 12-yard run in the third quarter.
Reggie Williams caught a 22-yard touchdown pass from Gray on Jacksonville's opening drive to make it 7-0. Williams was wide open in the corner of the end zone for the easy score.
Undrafted rookie Darius Walker scored his first career touchdown on a 1-yard run in the fourth quarter to put the Texans up 42-21.
The Jaguars set several team records in the loss. The four touchdown passes Sunday gave them 28 for the season to outdo the 24 they had in 1998. They also broke another record from 1998 with 50 touchdowns this year.
Notes: The win was Houston's first in AFC South play. ... Williams' 10th touchdown reception extended his single-season team record. He has caught a touchdown pass in a team-record four straight games.
