DeNesha Stallworth also had 21 points for the Wildcats (12-1), who came out sluggish after Friday's 90-23 rout of Alcorn State in which they set a school record for fewest points allowed. Kentucky trailed just twice early on but didn't gain its usual comfortable lead until late in the game.
O'Neill's play on both ends helped wear down Marist. The sophomore guard shot 7 of 11, including 4 of 7 on 3-point attempts, to easily surpass her previous best of 13 points. O'Neill also set career highs with four steals and four 3-pointers.
Kentucky scored 35 points off 27 Marist turnovers.
Elizabeth Beynnon had 15 points for the Red Foxes (5-6), who fell to 1-17 against ranked opponents.
The Wildcats had a tough act to follow after crushing Alcorn State. They also set a school record Friday by holding the winless Braves to 20 percent shooting.
Marist offered much more of a challenge, having won the Metro Atlantic Athletic Conference the past seven seasons. The Red Foxes had four players averaging at least nine points.
Nearly five minutes passed before Beynnon scored Marist's first field goal, but that was all the Red Foxes needed to get warmed up and stay close to Kentucky through much of the first half. Physical defense helped Marist, which disrupted the Wildcats' passing and movement.
Marist's problem was containing Stallworth, who scored six of Kentucky's first eight points off layups and 12 of the Wildcats' first 28 overall.
Kentucky got a brief scare when A'dia Mathies went out in the early minutes after hitting her head on the floor during a loose-ball scramble. The senior went to the locker room for observation but returned about four minutes later.
Mathies left the game again with 3:54 remaining in the first half, this time holding her left wrist after being tied up under the basket. She came back to start the second half.
Kentucky's deep bench filled the void in Mathies' absence and helped the Wildcats keep some distance from the stubborn Red Foxes.
The Red Foxes got as close as eight twice in the final 7 1/2 minutes before Stallworth's three free throws put Kentucky up 63-52.