The Colts trailed by 18 points late in the third quarter but Luck and Hilton teamed up on scoring strikes of 10, 58 and 9 yards to pull out the victory.
After their second touchdown pulled Indianapolis to within 24-19 with 9:54 left, the Colts got the ball back with 6 minutes remaining and Luck marched them 52 yards, capped by a go-ahead, 9-yard TD pass to Hilton.
Luck finished 18-of-40 for 271 passing yards and no interceptions while Hilton made seven grabs overall for 121 yards as the AFC South-leading Colts (6-2) came off a bye week with their fifth win in six games.
Johnson finished with nine grabs for 229 yards.
Texans Coach Gary Kubiak was hospitalized after collapsing along the sidelines during halftime of the contest.
"All his vital signs are good; he did not have a heart attack but they're still checking on him," Texans defensive coordinator Wade Phillips said.