Gary Cark became the 51st player in program history to reach 1,000 career points with 13 points and 11 rebounds.
Justin Jenifer had 15 points and five assists for the Bearcats, who extended their home-court winning streak to 27. They went 18-0 last season at Fifth Third Arena.
The Bearcats are playing their home games on the campus of Northern Kentucky University this season while Fifth Third undergoes an $87 million renovation.
Savannah State, which is moving to Division II by 2019, was led by Austin Dasent who scored 14 points.
The Tigers led the nation in 3-point attempts and makes last season and they began Friday's game by hitting 3 of 4 from behind the arc to build an early lead.
It took a while for the Bearcats to get going before a Friday sparse afternoon crowd. But Savannah State went scoreless for nearly three minutes, and Cincinnati went on a 10-0 run, capped by Clark's layup for a 35-21 lead.
Jenifer's lob to Tre Scott for a dunk gave Cincinnati a 17-point lead late in the half. The Bearcats led 60-40 at halftime with the teams combining for 18 made 3-pointers.
Cincinnati came out sluggish after halftime and the Tigers cut the deficit to single digits on a layup and two free throws by Ty'lik Evans with 12 minutes left. Evans had 11 points.
The Bearcats were scoreless for more than four minutes and Savannah State got within 69-62. But the Bearcats pulled away with a 17-1 run over three minutes.
NOTES: It was the most points scored by the Bearcats since a 119-68 win over Fairleigh Dickinson on December 17, 2016. ... Friday's game is part of the Cayman Islands Classic. Both teams travel to the Island later this month but compete in separate brackets. ... The Bearcats lead the all-time series 2-0. Cincinnati defeated the Tigers 54-41 on Nov. 24, 2010 at Fifth Third Arena.