Playing on its own floor, top-ranked Kentucky was able to get by a lesser challenger despite being without its point guard.
Kentucky (7-0) was without Ulis for Monday's 75-63 home win against Illinois State due to a hyperextended right elbow, and he may be out again.
Isaiah Briscoe scored a team-high 18 but the team seemed out of sync sans Ulis, who is averaging 13.2 points and 4.3 assists. The Wildcats recorded a season-low eight assists and committed 15 turnovers.
Ulis has committed only six turnovers over his last five games while playing 155 minutes.
"It was a big difference. We missed him out there," Briscoe said. "He's our leader and floor general."
John Calipari and company were encouraged by the play of Marcus Lee, who responded to coming off the bench for the first time with season highs of 13 points and 12 rebounds. Lee had been held to as many points and only three more rebounds over his previous three games combined.
This is the first in a home-and-home series with UCLA visiting Lexington next December. Kentucky dismantled the Bruins in an 83-44 victory on Dec. 20 in Chicago, outscoring them 41-7 in the first half after a 24-0 game-opening run.
UCLA was limited to 26.8 percent shooting - its worst showing in 11 years - and Ulis had seven points, seven rebounds and six assists in 18 minutes.
That marked the Bruins' fifth straight loss to a top-ranked team since a 96-89 overtime win against No. 1 Arizona in the 2003 Pac-10 Tournament.
"Last year was an outlier," Calipari told the school's official website. "I had a ridiculous team. And they would go into a game like that to smoke somebody ... They would go in with that mentality. This team is, we don't have that mentality."
The Wildcats are still outscoring opponents by an average of 17.4 points and their closest result was an 11-point victory against then-No. 5 Duke on Nov. 17.
UCLA (4-3) bounced back from back-to-back losses to Kansas and Wake Forest in Maui by returning home for a 77-45 win against Cal State Northridge on Sunday. The Bruins, who hit a season-high nine 3-pointers, led by 17 at halftime after being outscored by 33 in the first half of the previous two games.
"In Maui we had a couple rough starts and that's been something that's happening to us," coach Steve Alford said. "It was part of the game plan to get ahead first, to punch first, and keep throwing punches."
Tony Parker had 14 points and 11 rebounds for already his fifth double-double.
The Bruins struggled defensively in their first encounter with an elite team, letting then-fifth ranked Kansas shoot 54.2 percent in a 92-73 loss Nov. 24. They've since held two opponents to 34.5 percent shooting, though a new issue has popped up - free-throw shooting. They were 8 for 14 against the Demon Deacons and 10 for 18 against Northridge.
Kentucky owns a 7-4 advantage in the all-time series and won the only previous meeting in Los Angeles, 68-66 on Dec. 4, 1959.