The loss kept Milan only two points ahead of Juventus at the top of Serie A, and gave the Turin side a chance to take the lead when it visited Palermo later.
Milan took the lead with a penalty from Zlatan Ibrahimovic in the 31st at the San Siro but Stevan Jovetic equalized in the 47th after taking advantage of a Milan defensive lapse.
Amauri then finished off an exchange with Jovetic for his first goal since transferring from Juventus in January.
It was the fourth consecutive match in all competitions without a win for Milan, which drew 1-1 with Catania last weekend between a draw and a loss in its two-leg Champions League tie with Barcelona.
"It wasn't a great week, but we've got to bounce back, because everything is still up in the air," Milan manager Massimiliano Allegri said. "We've got to accept the result, knowing that there are still many games remaining and everything is still undecided."
The one bit of positive news for Milan was the return of forward Antonio Cassano, who came on in the 84th for his first appearance since undergoing minor heart surgery in November.
Elsewhere, Inter Milan drew 2-2 with 10-man Cagliari in its second match under new manager Andrea Stramaccioni.
In a match played in Trieste because of a dispute between Cagliari and its city council over renovating Sant'Elia Stadium, Davide Astori put Cagliari ahead with an acrobatic effort five minutes in and Diego Milito equalized a minute later, slipping behind the defense and spinning around before finding the target.
Chilean forward Mauricio Pinilla restored Cagliari's lead with a bouncing header in the 61st but was then shown his second yellow card for excessive celebrations and Esteban Cambiasso drew Inter level again three minutes later, taking a pass from Diego Forlan and scoring with a difficult shot using the outside of his foot.
Also, Udinese beat Parma 3-1 to draw level with Lazio for third place, which carries the final Champions League berth. Ghana forward Kwadwo Asamoah scored twice for Udinese and Antonio Di Natale also found the net for his 20th goal of the season, second only to Ibrahimovic's 23.
Lazio hosted fifth-place Napoli later.
Roma's chances of finishing third took a major hit with a 4-2 loss at Lecce, which is still in the relegation zone. Colombian forward Luis Muriel and David Di Michele each scored twice for Lecce, which led 4-0 before Bojan Krkic and Erik Lamela added late goals for the visitors.
In other matches, United States international Michael Bradley scored his first Serie A goal as Chievo Verona beat 10-man Catania 3-2; Mattia Destro scored an added-time winner in Siena's 2-1 win at Atalanta; Bologna was held 0-0 at last-place Cesena; and Giuseppe Mascara replied to Rodrigo Palacio in a 1-1 draw between Novara and Genoa.
All 10 Italian league matches were being played on Saturday due to the Easter holiday.
