"We felt like going into this game, that this is a game we should dominate," tackle Eric Winston said. "I feel like we did. We're finding our groove. Right now, we're feeling pretty good, and we've got to keep it moving."
The Texans (6-3) finished with a franchise-record 261 yards rushing and had a pair of 100-yard rushers for the second time in three games. They moved three games over .500 for the first time, and have now won three in a row without Johnson, who's missed five games with a right hamstring injury.
Houston used the same formula it employed in a 41-7 win at Tennessee two weeks ago. Foster and Tate also both ran for 100 yards in that game, and the defense held the Titans' offense to 11 first downs and 148 yards.
The Browns (3-5) totaled 10 first downs and 172 yards. Houston's defense has held the last three opponents under 200 yards, continuing its transformation under new coordinator Wade Phillips.
"This defense is very motivated," linebacker Brian Cushing said.
The Texans kept constant pressure on Colt McCoy, who was making his first NFL start in the state where he starred in college. McCoy was sacked four times and completed only 14 passes for 146 yards with an interception.
"They came from the first snap to the last and it's frustrating," McCoy said. "They were able to create a lot of pressure up front. At times, it was hard to overcome."
McCoy also got little support from the Browns' running game, hit by injury and controversy in recent weeks.
Chris Ogbonnaya, signed off the Texans practice squad less than a month ago, fumbled on his first carry and finished with 28 yards in place of injured running backs Peyton Hillis and Montario Hardesty.
Browns coach Pat Shurmur said Hillis will undergo treatment Monday after aggravating his strained left hamstring Friday. Shurmur said the Browns "have not discussed" putting the beleaguered Hillis on injured reserve, a move that would end his stormy season.
Hillis, in the final year of his rookie contract, spoke publicly about negotiating a new deal. He missed a game with strep throat, then was injured a few weeks later.
Shurmur dismissed the notion that Hillis has become a distraction.
"When a guy's not there for whatever reason, and in Peyton's case he's injured, you move on," Shurmur said.
The Texans scored on their opening series for the sixth time this season. Matt Schaub went 4-for-4 and Tate weaved his way through the Browns' defense for a 27-yard touchdown run.
Ogbonnaya lost the ball on Cleveland's first play from scrimmage, defensive end J.J. Watt recovered at the Browns 28, and Schaub scrambled for another score for a 14-0 lead less than 8 minutes into the game.
"We started very fast, both sides of the ball," Houston coach Gary Kubiak said.
The Browns have scored only six points in the first quarter this season, and McCoy said Cleveland had to scrap its original game plan when Houston took the quick lead.
"We spend the whole week working on the run game, play-action, things that you're going to do," McCoy said, "and then both times you have to completely abandon that and get into something else because you're down two touchdowns. We're not good enough to overcome that."
Houston's final rushing total surpassed the team record, set in last year's opener against Indianapolis, when Foster rushed for 231 yards by himself.
Tate and Foster traded carries in this one, with each breaking his share of long runs.
Foster has 24 career rushing TDs, a team record. ... Houston has outscored its opponents 148-45 in the first half this season. ... The Browns have been outscored 58-6 in the first quarter this year. ... Former President George H.W. Bush performed the ceremonial coin flip before the game.