HOUSTON  — The Houston defense made a statement Saturday, and the Cougars think they finally made their case to get into the polls.

Case Keenum was 30 of 37 for 304 yards and three touchdowns in just over three quarters to lead the Cougars to a 56-3 win over East Carolina on Saturday night.

Patrick Edwards caught 12 passes for 133 yards and two touchdowns, Charles Sims rushed for 84 yards and two touchdowns and Michael Hayes had 60 yards and a touchdown to lead Houston (6-0, 2-0 C-USA).

Bryce Beall added 47 yards and a score, and Tyron Carrier had seven catches for 53 yards and a touchdown for Houston, which had 572 total yards.

Houston enters its bye week as one of 13 undefeated teams, but remains just outside of the top 25 after being leapfrogged the last two weeks. Houston is 6-0 for the first time since 1990.

“We’re probably not the best team in the nation, but we are pretty close I guess,” Houston coach Kevin Sumlin said. “We can’t be any closer than we were last week.

“We talked as a team of what our goals are, and if we continue to win, those things take care of themselves. We don’t control that (the polls). We control what we do every week and go out and play. We want to win conference championships and be a top 25 team.”

Houston’s defense finished with four interceptions and nine sacks and held the Pirates to 284 total yards, including 21 rushing yards. Houston shut out Georgia State 56-0 two weeks ago.

“We were trying to play a complete game,” said Phillip Steward, who had two interceptions. “We were trying to get another shutout.”

Dominique Davis was 13 of 23 passing for 169 yards and three interceptions and Lance Lewis caught five passes for 73 yards for East Carolina (1-4, 1-1 C-USA). Torrance Hunt had 64 yards on 11 carries for the Pirates.

“This one is on me,” East Carolina coach Ruffin McNeill said. “We got beat by a better team tonight. They outplayed us on both sides of the ball . . . we faced one of the best quarterbacks I’ve faced in a long time in Case Keenum. He did a great job orchestrating his offense.

“We have to rebound from it. This was probably the worst game we’ve played as a football team this year. I thought we made a lot of mistakes and as a team we didn’t play very well.”

Keenum passed former Texas Tech quarterback Graham Harrell for second on the NCAA all-time passing yards list and now has 15,895 yards. He broke out of a tie for third with former Heisman Trophy winner Ty Detmer of BYU on the career touchdown passes list and now has 124.

Keenum completed his first 10 passes and threw touchdown passes of three yards and eight yards to Edwards in the first and third quarters, respectively, and found Carrier for a 27-yard strike to begin the fourth.

Keenum gave credit to his defense.

“Our defense did an incredible job tonight,” he said. “They made stops on third down, and that was huge. They gave us the ball back. We executed pretty good on offense. We are getting better as we go along, and we do better executing early.”

Beall put Houston up 7-0 with 9:43 left in the first on a 1-yard touchdown run capping a 15-yard, 80-play drive.

Michael Barbour cut the lead to 14-3 with a 54-yard field goal with 5:48 left in the opening quarter, but Houston upped the lead to 21-3 with Sims’ 5-yard run to begin the second quarter. Sims added a 4-yard touchdown run later in the second, and the Cougars led 35-3 at the half.

Hayes ran it in from 19 yards out to begin the third, and Cotton Turner had an 8-yard run to cap the scoring late in the fourth.

A week after allowing 42 points and over 500 yards against UTEP, Houston held East Carolina without a touchdown for the first time since 2009. Defensive lineman David Hunter said every win is a statement win, and being in the top 25 would be nice to see.

“I’m not really concerned about that,” said Hunter, who was credited with half of a sack. “All I want to do is win. Every game we play that we win is a statement . . . I do think this win was a statement, but so was the UTEP game and the Georgia State game. Every game we play, I feel like we go out there to make a statement.”