Jones, who was 13 of 17 for 197 yards, hit tight end Lawrence Cager on a 9-yard TD pass and Darius Slayton on a 54-yard catch and run as the Giants (7-2) tallied on their opening possession of each half in building a 14-3 lead.
Barkley, who had a career-high 35 carries, scored from 2-yards out in the third quarter after the Texans (1-7-1) closed to 14-10.
The Giants defense preserved the win, forcing two red-zone turnovers in the fourth quarter. Linebacker Jaylon Smith recovered Dameon Pierce’s fumble at the 11-yard line and Dane Belton intercepted Davis Mills’ pass in the end zone, one play after Houston lost a TD pass to Brandin Cooks because of a holding call.
Mills (22 of 37 for 319 yards) threw a 12-yard touchdown pass to Nico Collins and Ka’imi Fairbairn kicked field goals of 38, 34 and 46 yards for Houston, which has lost four straight.
The last field goal cut the lead to eight points with 7 seconds to play but Adoree Jackson recovered the onside kick to seal the win.
Pierce ran for 94 yards and had two catches for 28 yards for the Texans.
The 7-2 start is the best for the Giants since opening 8-1 in 2008. They are hoping to make the playoffs for the first time since 2016.
Cager was elevated from the practice squad for the game and the TD catch was the first of his brief four-game career, three with the Jets. He also recovered an onside kick after Fairbairn’s second field goal. … Texans TE Jordan Akins had three catches for 72 yards. … Slayton finised with three catches for 95 yards.
No injuries were announced during the game.
Texans: Return home to play the Commanders on Sunday.
Giants: Host Lions on Sunday.