Jacksonville, which has never had a winning record after dropping its first two games, was far from competitive in the latest meeting.
The Texans gained 242 yards in the first half while building a 17-0 lead. Foster ran for 69 yards and a score. Tate added 49 and a touchdown. Matt Schaub, using mostly short throws, picked apart Jacksonville's defense.
The Jaguars were even worse on offense, finishing with a franchise-low 117 yards.
Blaine Gabbert played like he did as a rookie, hurrying throws, missing open receivers and showing little pocket presence. Gabbert completed 4 of 11 passes for 13 yards in the first half, was sacked twice and had two balls batted down at the line of scrimmage both by J.J. Watt.
Gabbert finished 7 of 19 for 53 yards his fewest passing yards as a starter and ended the day standing on the sideline with an ice pack on his left thigh. He played one series in the fourth quarter before giving way to backup Chad Henne.
Jacksonville had 43 yards in the first half, the third-fewest in franchise history.
The Jaguars showed some life to open the second half, turning good field position into a touchdown. Gabbert hooked up with Laurent Robinson for 32 yards, and then found Maurice Jones-Drew in the flat for a 5-yard score. Jones-Drew had Bradie James all sorts of turned around on the play.
It was Jones-Drew's 75th career touchdown. He joined Randy Moss, Tony Gonzalez and Antonio Gates as the only active players with at least 75 TDs.
But the Texans answered, driving 80 yards in 17 plays. Tate's 2-yard plunge made it 24-7 in the third quarter.
Houston was sluggish to start its opener against Miami and even got booed before converting three consecutive turnovers in the second quarter into 24-3 lead.
The Texans had no such problems in Jacksonville.
The Jaguars played without cornerback Derek Cox and linebacker Daryl Smith, but more pressing injuries came on the other side of the ball. They were without left guard Eben Britton and right tackle Cam Bradfield.
With four offensive linemen already on injured reserve, Jacksonville turned to veteran Herb Taylor to start at left guard. Taylor practice just three times this week none in full pads and hadn't played in a game since 2008.
With Taylor and Guy Whimper starting, it was obvious the Jaguars wanted to try to run the ball early and often. Of course, that got thrown out the window as soon as Houston built its early lead.