Foster's performance on 28 carries gave him 3,299 yards for his career, vaulting him over Domanick Williams for Houston's club record.
Foster also made six receptions for 37 yards while Ben Tate added a pair of scores on 12 carries for 74 yards in the victory.
Matt Schaub passed for 195 yards on 26-of-35 passing efficiency as the Texans (2-0) won a second straight to open a season for the third straight year.
Jacksonville (0-2), meanwhile, could manage only a club-record-low 117 total yards of offense as Blaine Gabbert completed just 7-of-19 passes for 53 yards and a touchdown.
Maurice Jones-Drew picked up 60 yards on 12 carries and made three receptions for the Jags.