Zeller's rights were later traded to Cleveland for a package that included No. 24 pick Jared Cunningham of Oregon State.
Otherwise, it was the Wildcats' night, starting with a hug between Davis and Kidd-Gilchrist after the first selection.
"My arm was shaking and my hands were sweaty. Got up and hugged Michael, my best friend, wanted to hug him for a minute," Davis said. "When my name got called, wanted to make sure he stayed close."
He did following Davis as the next player to climb onto the stage and shake Commissioner David Stern's hand.
Kentucky's fourth first-round pick was at No. 29 with Marquis Teague, another freshman, who is headed to Chicago as a possible replacement for the injured Derrick Rose. Doron Lamb went 42nd to Milwaukee and Darius Miller was 46th to New Orleans.
Only the University of Nevada, Las Vegas in 1977 had six players drafted but none in the first round.
John Calipari has been criticized for recruiting "one-and-done" players, they stay the required one year and leave, but he looked thrilled hugging his two stars at the start of the night.
It's been a long time since a school made such an impact at the top of the draft.
University of California, Los Angeles had the Nos. 1 and 3 picks in 1969, when Milwaukee took Kareem Abdul-Jabbar then Lew Alcindor and Lucius Allen went third to the Seattle SuperSonics.
The 2.05-meter (6-foot-10) Davis averaged 14.2 points, 10.4 rebounds and 4.7 blocks, becoming a dominant defender after growing 7 inches from the start of his junior year of high school.
A season after the Hornets traded longtime star Chris Paul, Davis is ready to be their centerpiece, since playing for the Wildcats means he's already accustomed to plenty of attention.
"At Kentucky we had it all the time, especially the six who played, we had the spotlight all the time," Davis said. "It really prepared me."
Charlotte, coming off a 7-59 season and the worst winning percentage in NBA history, had been open to moving the No. 2 pick if it found the right deal. Instead, Michael Jordan's team went with Kidd-Gilchrist, whose selection by the Bobcats was loudly cheered.
Though he and Davis talked before the draft, they didn't discuss the history the Wildcats were about to make.
"No. I was shocked at first," Kidd-Gilchrist said. "I was shocked. But no, we didn't. We didn't at all."
Florida's Bradley Beal went third to Washington, making it three SEC freshman in the first three picks. Cleveland followed with the surprisingly early pick of Syracuse sixth man Dion Waiters at No. 4.
Thomas Robinson of Kansas, who hoped to go second, fell to Sacramento at No. 5. Portland took Weber State's Damian Lillard at No. 6 with its first of two lottery picks, and Barnes was taken seventh by Golden State.
After Washington's Terrence Ross went to Toronto and Connecticut's Andre Drummond to Detroit, the Hornets rounded out the top 10 by taking Duke guard Austin Rivers with a pick they acquired in the Paul trade. Rivers hugged his father, Boston coach Doc Rivers, who came to be with his family instead of with the Celtics, who owned two later first-round picks.
Davis was the only clear-cut pick entering the draft, and there were some early surprises. Players such as Waiters and Ross went higher than expected, while Robinson dropped to the Kings.
-AP