Yates, the Texans' third-string signal-caller, was forced into the game when Leinart -- himself subbing for the injured Matt Schaub -- was knocked out of the contest in the first half with a shoulder injury.
He went 8-of-15 through the air for 70 yards, while Arian Foster returned from a hamstring injury to gain 65 yards and score a touchdown for the AFC South-leading Texans (8-3), who notched their fifth straight win.
Foster, who has missed six games, also caught two passes for 22 yards.
Maurice Jones-Drew gained 99 yards on 18 carries for Jacksonville.
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