The Jaguars improved to 4-9 in the National Football League season as they halted the franchise's worse losing streak at home by winning there for the first time since November 2012.
"We had opportunities and our guys really believed in themselves," said Jaguars coach Gus Bradley. "To come out and finish like that is quite a tribute to them.
"The biggest challenge for us is to keep doing what we are doing. Stay true to who were are and what we are doing. We are a young team so we don't want to get too caught up in things."
Maurice Jones-Drew rushed for 103 yards on 14 carries before leaving with a hamstring problem. Marcedes Lewis, Cecil Shorts and Jordan Todman each caught touchdown passes for the Jaguars, who have won three in a row for the first time since 2010.
Quarterback woes continue to haunt the error-prone Texans. They have dropped a franchise-record 11 straight games after an impressive 2-0 start.
"It has been a gut-wrenching experience," said Texans coach Gary Kubiak.
Case Keenum threw 16-of-29 passes for 159 yards, one touchdown and an interception before being replaced in the third quarter.
Matt Schaub stepped in and completed 17-of-29 passes for 198 yards and one touchdown but he also had a key interception late in the game.
Andre Johnson caught 13 passes for 154 yards for the Texans, which committed 14 penalties for 177 yards. Garrett Graham caught eight passes for 73 yards and a touchdown.