Memphis improved to 9-0 for the first time since 1985-86, when the Tigers won their first 20 games, a school record. This one didn't come so easily.
Struggling Cincinnati (4-6) kept it close by taking advantage of two second-half technical fouls and the Tigers' inability to sustain anything for more than a few minutes.
Deonta Vaughn scored 20 points for the Bearcats, who are off to their worst start in 22 years.
Cincinnati was coming off its most inspired performance, a 64-59 loss to crosstown rival Xavier a week earlier. The Bearcats didn't back down in that rough-and-tumble game, and came away convinced that they had grown up as a team.
Against another old rival, they initially went back into their shell.
Memphis got a lot of open shots on the perimeter early and took advantage, making seven of its first 12. The Tigers pulled ahead 26-14 and seemed to be ready to take control. Instead, they eased up, lost most of their lead and had to sweat it out.
The Tigers failed to score on their last five possessions of the first half, when they had two turnovers and missed three shots. Cincinnati's confidence grew during an 11-1 run that culminated with Jamual Warren 's jumper at the buzzer that trimmed the lead to 33-32.
It was a significant development for the off-target Bearcats, who had shot 36 percent from the field in their last three games, all losses. They went 13-of-27 in the first half against a team that normally prides itself on pressure defense.
Rose got the Tigers back on solid footing, hitting a 3-pointer and making two free throws to open the second half. Cincinnati also slipped back into its shooting doldrums, missing its first eight attempts.
Still, Memphis struggled to put the Bearcats away.
John Williamson's three-point play gave Cincinnati its first basket of the half and cut it to 44-40, getting the less-than-capacity crowd back into the game. Rose asserted himself again, making another 3-pointer, and Willie Kemp 's three-point play off a fastbreak rebuilt the lead to 50-40.
Andre Allen made a three-point play and two 3s that helped Memphis build its biggest lead, 65-50, with 6:49 left. Two technical fouls - one on forward Joey Dorsey , another on coach John Calipari - blunted the momentum. Memphis also missed four consecutive free throws, giving Cincinnati a final chance.
Vaughn's 3-pointer cut it to 68-62 with 3:50 to go, but Williamson missed a dunk that could have increased the pressure. Finally, Rose hit a 3-pointer from the right wing that made it 73-64 with 1:52 to go.
Memphis has won its last three games against Cincinnati, with a freshman playing the leading role all three times. Two years ago, Antonio Anderson had career-high 32 points against Cincinnati. Last season, Willie Kemp scored 21 in an 88-55 win.