HOUSTON -- Before doubt could creep in and render what happened last week moot, and before concerns over early errant passes could undermine the progress shown leading the way to victory in his first start with his new team, San Francisco 49ers quarterback Jimmy Garoppolo caught fire.

And once Garoppolo got rolling, so too did the 49ers.

Garoppolo was poised under duress and the 49ers won consecutive games for the first time since 2014 with a 26-16 victory over the Houston Texans on Sunday at NRG Stadium.

Garoppolo passed for a career-high 334 yards and produced his second touchdown pass with the 49ers, a 6-yard strike to tight end Garrett Celek with 1:53 left in the third quarter. That pass snapped a 16-16 tie and helped lift the 49ers (3-10) to their second consecutive road triumph.

San Francisco last won in successive weeks in November 2014. Garoppolo engineered a game-winning drive in the fourth quarter last week at Chicago. He didn't take as long to get going against Houston (4-9), leading the way on five consecutive scoring drives starting in the second quarter.

"You've got to have guys who are fearless, can hang in there and keep their eyes down the field," 49ers head coach Kyle Shanahan said. "He (Garoppolo) does that very, very well. But he also has the foot quickness and agility to get out of there and extend some plays."

The Texans sacked Garoppolo twice and hit him nine additional times, with standout linebacker Jadeveon Clowney recording four hits on Garoppolo alone. But Garoppolo stood firm against that pressure, overcoming an early interception and completing 20-of-33 pass attempts.

"That was a tough group," Garoppolo said. "Jadeveon Clowney is one of the best in the league at what he does, but I think our guys played great today. You're going to give up some things here and there, but overall, I think it was a phenomenal day for those guys."

San Francisco kicker Robbie Gould drilled field goals of 52, 35, 25 and 41 yards to aid the cause.

The 49ers knocked out Texans quarterback Tom Savage in the second quarter, but backup T.J. Yates engineered consecutive scoring drives upon entering the game, capping both with touchdown passes to DeAndre Hopkins. The latter gave Houston a 16-13 lead in the third quarter.

Hopkins finished with 11 receptions for 149 yards and two touchdowns, but his fumble in Houston territory late in the fourth quarter resulted in the fourth Gould field goal. Yates passed for 175 yards and produced a 100.6 passer rating in his first extended action since 2015.

But Hopkins had just one catch for five yards in the fourth quarter. The 49ers committed to bracketing him all over the field and effectively shut down the Texans offense down the stretch.

"You can't really force him the ball when they're bringing the safety down, bringing the safety over the top or they're trailing from behind," Yates said of Hopkins. "They were doing everything they could to put two and sometimes three guys over in his area. We've got to do a better job of distributing the ball around because if they do that to him there should be other guys open."

Receiver Marquise Goodwin recorded six receptions on 12 targets for 106 yards while running back Carlos Hyde averaged 5.6 yards per carry and produced 78 rushing yards for the 49ers.

After mustering four first downs over their opening four possessions, the 49ers caught fire in the second quarter after Garoppolo completed a 32-yard pass to Goodwin that set the stage for the first Gould field goal, a 52-yarder that pulled San Francisco even at 3-3 at the 6:31 mark.

Their third scoring drive was particularly impressive, with the 49ers covering 62 yards in six plays and 54 seconds and Gould nailing a 35-yard field goal as the first half expired. The Texans erased that 13-9 halftime deficit on their first drive of the third quarter, but the 49ers kept rolling behind Garoppolo and surged ahead for good in the waning moments of that period.

"They did some good things," Texans head coach Bill O'Brien said of the 49ers. "Carlos Hyde's a good back. Their offensive line blocked I thought pretty well. I thought Jimmy made some good throws."

NOTES: Texans LT Kendall Lamm suffered a concussion in the first quarter and did not return. Lamm became the fifth Texans player in two weeks to depart a game with a concussion. The Texans later lost QB Tom Savage to a concussion just prior to the intermission. ... 49ers K Robbie Gould converted all four of his attempts to extend his string of consecutive field goals made to 14. ... With two scoring grabs, Texans WR DeAndre Hopkins matched his franchise single-season record of 11 touchdown receptions set in 2015.