Jones-Drew had his first 100-yard game of the season and scored three touchdowns to lead the Jaguars over the mistake-prone Texans, 31-24 on Sunday.
Jones-Drew scored the go-ahead touchdown on an 8-yard run early in the fourth quarter and finished with 119 yards rushing.
"Each play we got better," Jones-Drew said. "Each time we got to the sideline we got better. We just kept believing in each other and that was the best thing about it ... they jumped out on us real quick. We just kept fighting back, fighting back. No one blinked."
Jacksonville became the third straight team to run over Houston's NFL-worst run defense. The Texans allowed 190 yards to the Jets, 240 to the Titans and 184 on Sunday.
Houston (1-2) had several chances to tie the game. The last came when Chris Brown's goal line fumble was recovered by the Jaguars (1-2) in the end zone. The Texans challenged but Jacksonville kept the ball.
"When you let down all your teammates, you can't put it into words," a distraught Brown said.
The Texans had a touchdown nullified two plays earlier when Kevin Walter was called for offensive pass interference.
The Jaguars were driving with a seven-point lead and 4 1/2 minutes left when Houston's Dunta Robinson forced a fumble by Mike Sims-Walker. Zac Diles recovered and the play was challenged, but the ruling on the field stood and the Texans got the ball.
The Jaguars forced Houston into a three and out after Clint Ingram tripped Matt Schaub for the sack with about six minutes left in the fourth quarter. Ingram jumped around after the hit while the normally stoic Jack Del Rio broke into a huge smile.
Houston had a first down at the 17 but had to settle for a field goal that tied it at 24 in the third after Schaub's run on third down came up one yard short.
Jacksonville took the first drive of the second half 83 yards, capped by a 1-yard touchdown run by Jones-Drew to regain the lead, 24-21.
Del Rio was impressed with his team's halftime adjustments.
"They had kind of gone into the end of the first half there and taken some momentum," he said. "Our team responded well, getting the ball coming out of the half, going down and getting a score there and letting them know that we were here, on a mission and that we had the resolve to be in a dogfight and win this thing."
Schaub threw for 300 yards in the game and had three touchdowns in the first half, but couldn't get anything going after halftime.
He found Owen Daniels on an 2-yard reception for his third touchdown pass to put Houston ahead 21-17 at halftime.
Houston kept that drive going with an 11-yard end around by Walter on fourth-and-1 from inside the 20.
A week after Chris Johnson blew by Houston's defense for three touchdowns of more than 50 yards, Jones-Drew scored his first touchdown on a 61-yard run. The score put Jacksonville ahead 17-14 in the second quarter.
"We're giving up some big, big plays and struggling to stop somebody," Houston coach Gary Kubiak said.
Walter put Houston on top 14-10 with a 9-yard touchdown catch in the second quarter. It was his first action of the season after sitting out the first two games with a hamstring injury.
Houston's Jacoby Jones scored for the second straight week on an 18-yard pass from Schaub that put the Texans up 7-3 in the first quarter. Jones lost his shoe on the catch before bounding over to his mother's front row seat behind the end zone for a hug.
Houston rookie Brian Cushing tipped one pass and broke up another, but a late hit penalty late in the third quarter helped propel the drive that put the Jaguars up 31-24.
Ernest Wilford looked to have scored on a 15-yard touchdown reception early in the second quarter. Kubiak challenged the call and after review, officials ruled that Wilford stepped out of bounds at the 2-yard line.
Jacksonville didn't take long to put that score back on the board when David Garrard ran in for the touchdown on the next play to make it 10-7. Garrard finished 214 yards passing.