CHAPEL HILL, N.C. -- Tyler Zeller scored in the paint and buried the free throws North Carolina desperately needed. John Henson locked down on Kentucky's top scorer. Larry Drew II even added a strong second half that helped his team hang in until the final horn.

For an afternoon, the Tar Heels showed some fight that has been missing around Chapel Hill for the better part of a year -- especially against a marquee opponent like the Wildcats (No. 11 ESPN/USA Today, No. 10 AP).

Zeller scored a career-high 27 points and hit the go-ahead free throws with 47 seconds left, helping North Carolina edge Kentucky 75-73 on Saturday in a matchup of two of college basketball's winningest programs.

Zeller scored 12 of the final 16 points for the Tar Heels (5-3) in a game that had five lead changes in the final 3 minutes before Kentucky's Doron Lamb missed a desperation heave for the win from near halfcourt as time expired. The Tar Heels have won six of the last seven meetings in a matchup of programs each with more than 2,000 all-time victories.

"You never can tell what 19-, 20-, 21-year-olds are going to take from something," North Carolina coach Roy Williams said. "But I know the scene in our locker room right after the game when I got in there was a fun time. Hopefully they'll understand that and realize what they have to do to get back there."

The Tar Heels struggled to match physical play from Minnesota and Vanderbilt in the Puerto Rico Tip-Off, then committed too many turnovers at Illinois (No. 21 ESPN/USA Today, No. 20 AP) in this week's ACC/Big Ten Challenge. Against the Wildcats (5-2), they dominated inside and matched their season-low of 12 turnovers.

Drew, who has struggled this year as the starting point guard, came up with a pair of critical free throws with 20.9 seconds left and scored all seven of his points after halftime.

It came down to a frantic final sequence, with neither team having a timeout left and the Tar Heels protecting a 74-73 lead with 5.6 seconds remaining.

Dexter Strickland made the first free throw but missed the second, and Darius Miller grabbed the rebound in traffic. He fired an outlet pass to reserve Jarrod Polson, who quickly sent the ball to Lamb for the final shot that missed everything and set off a roar from a relieved crowd.

"It's not one of those games where we can be content that, 'OK, we beat Kentucky," Zeller said. "That doesn't make your season. That helps make your season."

Still, North Carolina shot just 41 percent, including 1 for 11 from 3-point range. The Tar Heels didn't manage a field goal in the final 6 1/2 minutes, but helped themselves by going 26 of 37 from the free-throw line for the game.

Kentucky didn't fare much better from the field, going 9 for 30 in the second half, and didn't get to the line nearly so often (21 attempts) to make up for it.

"It was two young teams," Kentucky coach John Calipari said. "There were some plays made where I just shook my head, and Roy said to me afterward, 'Not really well played, but a good game.' And I said, 'Well said, Coach. Well said.' But we've got a lot of work to do. I've got a young team, and we didn't have leadership on the court."

Zeller ended up as the steady hand late, hitting all six of his free throws in the final 90 seconds. The 7-foot junior also had a career-high 11 rebounds and matched his high of five blocks. He was a big part of the Tar Heels' dominance in the paint, where they outscored the Wildcats 34-14 and hounded leading scorer Terrence Jones into a miserable game.

Henson, a 6-10 long-armed sophomore, added 13 points and 12 rebounds while leading the defensive effort on Jones, who came in averaging nearly 21 points and 10 rebounds.

Jones finished with nine points and six rebounds on 3-for-17 shooting -- including 0 for 7 after halftime -- before fouling out with 3:04 left.

"I sensed him getting a little angry and a little upset," Henson said. "As a player, you like to see that and you feed off that."

Lamb scored a season-high 24 points for Kentucky, while fellow freshman Brandon Knight scored 15 points before becoming the last of four Wildcats to foul out.

"It hurt us a lot," Lamb said of the foul trouble. "Josh and Terrence had a couple of dumb fouls at the end that were stupid fouls. We need them at crunch time."