Empoli keeps Milan winless at home
Dida has been under scrutiny since his theatrics at Celtic in the Champions League where he fell to the ground after being touched by a fan and acted as if he was hurt.
Dida has been banned for two games by UEFA, and Milan have appealed.
Before Sunday's game, Dida walked to every corner of the ground and bowed to the supporters as if to apologise for his antics in Scotland and the Rossoneri faithful applauded.
However, the setback was another blow for Milan's fading title hopes as they are now 10 points behind city rivals Internazionale in what owner Silvio Berlusconi admits has been the worst period of his 21-year reign.
Milan went into the game hoping to win their first league encounter at the San Siro since April 21 and were boosted by the return of captain Paolo Maldini.
Maldini had not played an official game for the Rossoneri since the Champions League final in Athens due to a knee injury.
Milan started strong and missed a golden chance to take an early lead with Marek Jankulovski's cross serving Filippo Inzaghi inside the box whose effort went wide.
Empoli were quick to reply but Luca Antonini's dangerous cross from the left failed to find a team-mate.
The visitors should have broken the deadlock on 14 minutes but Davide Moro failed to beat Dida on a one-on-one with his close-range effort going high over the crossbar.
At the other end, Jankulovski failed to capitalise on Inzaghi's great assist as he struck high over the bar.
Shortly after the half-hour mark, Dida was called into action to save Saudati's right-footed strike.
The hosts could have gone into the break with a 1-0 lead had Inzaghi been able to find the finishing touch inside the area after a clever assist from Andrea Pirlo.
Milan picked up where they left off but still struggled to find the finishing touch, with Inzaghi unable to get behind Oddo's cross.
The hosts had a lucky escape soon after, with an unmarked Saudati wasting a great opportunity to put his team in front, with his close-range header going wide of Dida's near post.
But Saudati made amends shortly after, nodding in Francesco Marianini's cross past Dida for a 1-0 lead.
The goal inspired Empoli who on the hour mark could have doubled their advantage had Dida not fully stretched to clear Saudati's strike from the edge of the area.
Milan coach Carlo Ancelotti reacted by bringing on three new players and his team carved out several scoring chances, the best of which saw Massimo Ambrosini's close-range effort met by a fine save from goalkeeper Daniele Balli.
Tuscan minnows Empoli held on for their first win on the road this season.
