Booker returned from a one-game absence to make all three long-range attempts and 5 of 8 overall on a day that Kentucky shot 57 percent from the field.
Kentucky never trailed and eventually built a 19-point second half lead, though North Carolina got within 66-57 midway through as Marcus Paige (14 points) warmed up from outside. The Wildcats answered with a 14-5 run over 5:56 for another safe cushion.
Aaron Harrison added 14 points and Trey Lyles had nine starting in Poythress' place.
Brice Johnson's 15 points led the Tar Heels, who won the rebounding battle 31-24 but found little success against the Wildcats' size.
Kentucky conquered another challenging opponent, no easy feat considering how Poythress' injury left a somber mood around the practice facility on Friday.
Players showed support for their injured teammate by wearing blue "Roar for 22" T-shirts during warmups, and Poythress entered on crutches to a loud ovation before a showdown between two of college basketball's three winningest programs.
From there Kentucky answered the on-court question about the injury's effect on its two-platoon system where Poythress started on the first unit. The Wildcats used it at times but mostly went with a combination of its nine-deep group of regulars.
Lyles quickly hit a jumper and remained on the court to play with his usual second platoon mates. That unit sparked a 16-8 lead as Booker and Tyler Ulis nailed successive 3-pointers against UNC's zone defense.
That set the stage for Kentucky's 6-of-12 first-half performance from long range with Aaron Harrison joining in late in the half. He entered the game in a 2-for-12 slump but made his first shot, and his relief gave way to confidence on his next two that swished through to bring a roar from the crowd and a 49-34 lead halftime lead.
He went on to finish 5 of 9 from the field and 3 of 7 from long range. Cauley-Stein grabbed six rebounds for the Wildcats, whose bench outscored the Tar Heels 33-19.
North Carolina: Paige became the 71st Tar Heel with 1,000 career points.
Kentucky: Last season's leading scorer, Los Angeles Lakers forward Julius Randle, came out to cheers to spell the "Y'' in Kentucky during a second-half timeout. Randle is out for the season with a knee injury.
North Carolina: Visits North Carolina-Greensboro on Tuesday.