Jones-Drew carried the ball 14 times to back Chad Henne, who completed 23-of-32 passes for 239 yards for the Jaguars (2-9).
With the result, Jacksonville tied the Texans for last place in the AFC South.
The Texans (2-9) continued their skid as Case Keenum was limited to 169 yards with an interception on 18-of-34 efficiency.
Dennis Johnson led Houston's rushing corps with 74 yards on 13 carries.
2014: The Year in Music [PHOTOS]