Antonio Anderson scored 10 points for the Tigers (16-0, 3-0 Conference USA), who have won 35 consecutive regular-season games and 26 in a row in league play.
Calipari wasn't happy about this one, though, often screaming at his team during timeouts for its lackadaisical effort.
"We're competing against us, no disrespect to Rice," Calipari said. "My job is not to coach against Rice, it's to coach against us. I know when we're competing and when we're not. I know the effort level we're capable of."
The Tigers went 7-for-31 from 3-point range (23 percent) and barely outrebounded the smaller Owls 42-41. Memphis won with its full-court defense, which forced the flustered Owls into 29 turnovers.
Rice started three freshmen and a sophomore and coach Willis Wilson has added three walk-ons in the last month to fill a roster ravaged by injuries. The highly touted Tigers still struggled at times, missing shots and getting beat to loose balls.
"We're supposed to be this monster team," Calipari said. "If you ask me, they outscrapped us, they outhustled us."
Paulius Packevicius had 13 points and 12 rebounds to lead the Owls (3-13, 0-3), who have lost six straight. Wilson conceded the Owls have no championship dreams, like the Tigers.
"For a team like Memphis, their goal is still way ahead of them," Wilson said. "Our goal is right here in front of us. But we have as much work to do to reach our goal as they do to reach theirs."
The Tigers' defense overwhelmed the Owls at the start, forcing three turnovers in the first two minutes. To make matters worse for the Owls, Packevicius, their leading scorer, picked up two quick fouls and went to the bench with 17:54 remaining in the half.
Memphis led 16-4 when Packevicius returned 3 minutes later and Mack's 3-pointer with 12:39 left stretched the lead to 15 points.
But after the Tigers' hot start, the Owls' half-court zone defense started giving the Tigers problems. Rice forward Suleiman Braimoh blocked a shot by Dorsey and Memphis missed 13 of 16 shots after building the big lead.
The Owls also found some holes in the Tigers' defense. Scott Saunders had a dunk and Lawrence Ghoram hit a 3-pointer to cut the deficit to 25-16. Two minutes later, Bryan Beasley's driving layup pulled Rice within 28-20.
"What happens with every team we play, they play to a level they haven't played all year," Calipari said. "If you don't come out and make them match your intensity, they outscrap you. That's what aggravated me today."
The Tigers finished the half with a 12-3 burst, started when Dorsey had a steal, a rebound basket and a breakaway dunk in a 20-second span. Memphis scored 21 points off 19 Rice turnovers in the half and held the Owls without a field goal over the final 4:46.
Memphis pushed the lead over 20 points in the opening minutes of the second half by forcing more turnovers that turned into easy baskets. Derrick Rose threw an alley-oop pass to Robert Dozier for a dunk with 14:47 left to put the Tigers up 52-28.
The Tigers kept adding to their lead despite missing 19 of their first 22 3-point attempts. Memphis missed nine consecutive 3-point tries before Mack connected with 11:26 left to put Memphis up 60-35.
Calipari took out his starters with 4:58 left and the Tigers leading 70-42.
The game drew a paltry crowd of 1,892 to Reliant Arena, Rice's main temporary home while on-campus Autry Court undergoes renovations.
