The loss spoiled the much-anticipated debut of Terrell Owens.
Owens, who was signed this offseason after spending the previous year and a half with the Philadelphia Eagles, finished with six receptions for 80 yards and a touchdown.
Owens keyed all three of Dallas' scoring drives, including a 21-yard TD reception with 1:54 to play that cut the lead the 24-17. However
Jacksonville recovered the onside kick and was forced to punt.
The Cowboys got the ball back with 51 seconds to play, but Drew Bledsoe's third-down pass was intercepted by linebacker Mike Peterson.
It was Bledsoe's third interception of the game and gave the Jaguars their ninth opening-day win in 12 seasons.
It also may have silenced critics who said the Jags made the playoffs last season only because of a weak schedule and that they would struggle to replace retired receiver Jimmy Smith.
Jacksonville hardly missed the five-time Pro Bowler.
Matt Jones caught five passes for 71 yards, including four in a row on the team's go-ahead touchdown drive in the fourth quarter. Reggie Williams had six receptions for 47 yards, and Ernest Wilford caught three passes for 58 yards.
Taylor was even better. The 30-year-old, oft-injured Taylor ran 21 times for 74 yards, including a 5-yard score with 3:13 remaining. He also caught six passes for 41 yards.
The Jaguars trailed 10-0 in the first quarter, and coach Jack Del Rio looked like he made a mistake playing dinged-up starters Peterson and Marcus Stroud. Both players missed tackles on the first two drives.
Owens, meanwhile, was the catalyst for the scores.
He had two catches on Dallas' opening touchdown drive and helped set up a field goal on the team's second possession. He ran a simple slant pattern on Dallas' first play from scrimmage, beat Rashean Mathis and gained 13 yards. Two plays later, he was open again for an 8-yard gain. The plays started a 70-yard drive that ended in Julius Jones' 23-yard TD run.
On the next possession, Owens drew coverage in his direction that allowed Jones to run wide open down the sideline for a 39-yard reception, setting up Shaun Suisham's 32-yard field goal.
Owens, benched by Philadelphia for the final nine games last season after griping about his contract and bickering publicly with quarterback Donovan McNabb, was released Owens in March and signed with Dallas four days later.
He missed most of training camp but vowed to be ready for the opener.
And he was, as the game started to look like it would become the T.O. Show. But the Jaguars adjusted their defense and held Owens to just two catches in the second half while putting constant pressure on Bledsoe.
When Bledsoe tried to rally the Cowboys, he threw two interceptions in the fourth quarter. He finished 16-of-33 for 246 yards with a touchdown and three picks.
"We had a chance to go up 17-0 and keep control of the game," said Bledsoe. "Once we let them hang around we started making mistakes and that's the story of the game."
Jacksonville's defense allowed 125 yards in the first quarter, but just 198 yards the rest of the way. The unit suffered a major loss, though, in the fourth quarter when defensive end Reggie Hayward tore his Achilles tendon and was lost for the season.
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