The victory was Houston's eighth in a row – a franchise best and a reversal of fortunes since losing the opening three games of the season.
It also marked the first time in NFL history that a team has recorded eight consecutive wins after a 0-3 start.
Lamar Miller added his name to the record books with a 97-yard touchdown run for the Texans in the second quarter – the longest run in team history.
The running back is now the only player ever in the league to have two career touchdowns of 95 yards or longer, having previously run 97 yards to score in 2014 for the Miami Dolphins.
Quarterback Deshaun Watson also impressed for Houston, completing 19-of-24 passes for 210 yards and two touchdowns, and rushing for a single-game career-high 70 yards on nine carries and a touchdown.
Demaryius Thomas scored his first two touchdowns as a Texan in his debut for the side.
Tennessee had led 10-0 early on thanks to Ryan Succop's field goal and Jonnu Smith's 61-yard touchdown run, but they could only add a second touchdown through Corey Davis in the third quarter as they fell to 5-6 for the season.