After opening the season with eight straight losses, the Jaguars have won four out of five including their last three. Two of those wins have come over Houston (2-11), which has lost 11 in a row and needs a victory in December to avoid equaling the worst record in franchise history.
Henne's two scoring throws put Jacksonville in front 14-0 and a 21-yard touchdown pass by receiver Ace Sanders to Jordan Todman with 6:12 left in the third quarter gave the Jaguars a 24-10 advantage.
Schaub began by guiding the Texans 76 yards to a touchdown that came on a 5-yard throw to Garrett Graham with 1:08 to go in the third. Schaub then directed Houston 55 yards in 11 plays and the Texans cut their deficit to four points on Randy Bullock's 31-yard field goal.
Houston's next drive, however, ran out of downs inside the Jaguars' 20-yard line and Schaub was soon intercepted in his own end of the field.
After that interception Jacksonville produced a field goal with 25 seconds left that accounted for the final score.
Henne completed 12-of-27 for 117 yards. Both Keenum and Schaub had a touchdown and an interception.