Antonio Di Natale and Dusan Basta scored second-half goals for Udinese who have managed to maintain last season's impressive form despite parting company with two of their most important players.
Milan were involved in a see-saw battle at Bologna, where Marco Di Vaio gave the hosts the lead, Clarence Seedorf and Zlatan Ibrahimovic replied for the title-holders and Alessandro Diamanti made it 2-2.
"The table looks beautiful, let us see how long it lasts," he said after Sunday's game. "It's a magical moment and I hope we can make it last as long as possible."
Udinese took 67 minutes to break down Chievo, finally scoring when 34-year-old Di Natale, last season's Serie A top scorer, found the net with a looping header from Mauricio Isla's pass.
Milan survived a penalty appeal in first-half injury-time when Seedorf appeared to block Diamanti's free-kick with his arm and the visitors escaped again when Di Vaio's shot hit the post after the restart.
It ran out one minute later, however, when Diamanti's low, 25-metre shot slipped through Amelia's hands for the equaliser.
"It's always annoying to concede goals and it's especially annoying because of the way we did it. For the second goal in particular, we made mistakes as a team," said Milan coach Massimiliano Allegri.
"Today the referee made mistakes against both teams. I didn't say anything after the game against Fiorentina when we had four decisions go against us and I won't comment now either."
