MEMPHIS, Tenn. (AP) -- This is what counts as a challenge these days for top-ranked Memphis: trailing at halftime to a team shooting well, even hitting from way beyond the arc.
The Tigers answered with smothering defense and pulled out what passes for a tight victory for this team.
Chris Douglas-Roberts scored 22 points and Memphis rallied from its first halftime deficit since Dec. 4 to remain undefeated with a 68-59 victory over Houston on Wednesday night.
This was the kind of game Memphis coach John Calipari wanted for his Tigers.
"If I have to raise my voice at this time of the year at halftime, then we're petering out," Calipari said of the 37-35 halftime deficit.
"I went in and I just said, 'This is what we needed. You're talking about a team that is playing for their lives. They outscrapped us, outrebounded us and made a few shots.' Some of them were like, 'Oh, my gosh.'"
The Tigers (24-0, 10-0) have won 47 straight games on their home floor, 53 in a row in the regular season and 33 straight in Conference USA.
Robert McKiver had 21 points for Houston (18-5, 7-2), which had won three straight.
The Cougars dropped to 2-11 against top-ranked teams. Houston hasn't beaten a No. 1 team since Feb. 18, 1978, against Arkansas.
Coach Tom Penders said he thought his Cougars gave the Tigers all they wanted despite falling short in their bid for the upset.
"But you've got to do a lot of things right. I don't think we were really worn down. I'm not saying we were full of zip and energy in the end ... I don't think we were exhausted. But they're a great team and one of the reasons they're a great team is they are 12 deep in quality," Penders said.
Tafari Toney had 14 points for the Cougars.
It was the first time the Tigers have trailed at halftime since Southern California led 29-24 in New York. Memphis won that game 62-58 in overtime.
Douglas-Roberts said he had read some comments by the Cougars and expected them to come out on fire.
"They had seven 3s in the first half, and we were lucky to be down two at halftime. The team hits seven 3s in the first half, you should be down about 15. But we knew they were going to have to do that the whole game," he said.
Houston, which had been 17-2 when leading at halftime, turned Memphis over twice in the opening minute of the second half.
But the Cougars lost their seventh straight in this series after losing their shooting touch, missing 13 of their first 14 and finishing 8-of-35 (22.9 percent) in the second half. McKiver, the Cougars' leading scorer, was 2-of-13 in the final 20 minutes.
McKiver said he tired with Memphis making him work harder for shots.
"They've got like 10 starters," McKiver said. "When they go to the bench, they don't really lose anything. That's a great asset for their team. That helps them close out games and go on runs like that."
Douglas-Roberts called McKiver, Houston's top scorer, good, which is why he was 4-of-8 from 3-point range in the first half.
"But you're going to have to hit those deep 3s with a hand in your face for 40 minutes, and that's tough," Douglas-Roberts said.
With fans on their feet in the opening minutes of the second half, Douglas-Roberts and Anderson helped Memphis take control with a 14-3 run.
Douglas-Roberts scored the first four points of the half and added a free throw. Anderson scored on a fast-break layup, hit a 3-pointer and hit two of three free throws for a 49-40 lead with 15:55 to go. Rose's 3 with 13:37 left gave the Tigers their first double-digit lead of the game at 54-44.
It didn't help that the Cougars, the nation's seventh-best shooting team at the line, only got there twice. Memphis, which had been ranked 324 out of 325 Division I teams in free-throw shooting, was 19-of-32.
Asked about the disparity at the line, Penders said all he knew was that Memphis won the game.
"They're a great basketball team. We tried to drive. ... We were driving it, and they were blocking a lot of them, too," Penders said. Memphis had nine blocks.
The first half couldn't have been much tighter as the teams swapped the lead 11 times with six ties, and McKiver put Houston ahead with his fourth 3-pointer with 1:04 left in the first half. Douglas-Roberts stole the ball from Toney in the final seconds to keep it tight.
The Cougars got Tigers senior Joey Dorsey into quick foul trouble, which helped them control the boards early. Dorsey, who had three rebounds in the first half, finished with 12 as Memphis had a 46-37 rebound advantage.