Azubuike led three players in double figures and was 11-of-14 from the field. The junior forward was 3-of-4 from 3-point range.
Rondo had a team-high five assists and was 8-of-9 from the free-throw line.
Kentucky shot 54 percent from the field and had 15 assists.
The Wildcats held a 41-38 halftime lead, but Hayes scored eight of Kentucky's first 10 points of the second half as the Wildcats slowly pulled away from the Norse.
Northern Kentucky narrowed the deficit to 51-49, but could get no closer as Kentucky went on a 14-2 run that pushed the lead to double digits at 65-51 with 8:50 remaining.
Then a 14-3 run gave Kentucky an 83-60 lead at the 4:44 mark of the second half.
Kentucky forced 26 turnovers, including 19 in the second half.
Northern Kentucky coach Dave Bezold said Kentucky's defense took its toll on his squad, especially in the second half.
"It's like standing in the ocean in blocks and the waves keep crashing on you and crashing on you," he said.
Azubuike scored 16 points in the first half and was 6-of-7 from the field, including 3-of-3 from 3-point range.
Northern Kentucky guard Mike Kelsey scored 18 of his game-high 27 points in the first half. an 18-10 lead with 13:35 remaining in the first half. Kelsey's 3-pointer gave the Norse an 18-10 lead with 13:35 remaining in the first half. He finished 7-of-10 from 3-point range.
"He can really shoot the ball," Kentucky coach Tubby Smith said. "He gets it off so quick, and it looks like every one of them is going in. He made a believer out of me."
Northern Kentucky held a 20-12 advantage with 12 minutes left in the half, but the Wildcats made eight consecutive free throws, including six in a row by Rondo that tied the score at 20-20.
Kentucky then scored 15 unanswered points, capped by Azubuike's 3-pointer that gave the Wildcats a 27-20 lead with 7:20 left in the half.
The Norse made 7-of-12 shots from long range in the first half and shot 46 percent from the field.