The setback piled the pressure on Milan manager Massimiliano Allegri whose team are stuck in mid-table on three points having lost two of their first three league games this season.
"To lose your first two home games of the season isn't pleasant," said an uncomfortable Allegri who declined to comment on his relationship with club vice-president Adriano Galliani.
Earlier, Cagliari's Marco Sau came off the bench to snatch a late headed goal in a fortunate 1-1 draw at Palermo.
Atalanta, who had two points deducted for their role in the latest match-fixing scandal, never let Milan relax with German Denis causing problems with his hold-up play and movement.
The Argentine, nicknamed The Tank because of his strength, could have opened the scoring after 20 minutes when he pounced on a Francesco Acerbi error but his shot hit the post.
Six minutes later Milan, yet to score at home this season following the sale of Sweden striker Zlatan Ibrahimovic to Paris Saint-Germain, could have scored themselves after forcing Andrea Consigli to make a spectacular double save.
First the keeper kept out Stephan El Shaarawy's long-range strike and then the rebound off Gianpaolo Bellini to prevent a comical own goal after the defender had raced back to clear.
The second half was short on chances with both sides seeming content to shoot from distance but Atalanta struck after 64 minutes when Cigarini raced onto a Denis lay-off and skidded a low shot across Christian Abbiati's body from 25 metres.
MORE AGGRESSIVE
Milan, who host Anderlecht in the Champions League on Tuesday, reacted by being more aggressive and would have equalised if Giampaolo Pazzini and Antonio Nocerino had connected with crosses with the goal at their mercy.
However, Atalanta could have doubled their lead with six minutes left only for Cristian Raimondi towaste the chance by shooting straight at Abbiati after a smart counter-attack.
Despite Milan's continued pressure, Stefano Colantuono's Atalanta side held on for a victory that puts them on two points, taking into account the two points they have been deducted, and lifts them out of the relegation zone.
Allegri is hoping the start of Milan's Champions League campaign can kick-start their stuttering season.
"I believe that we have to continue to work, but fortunately on Tuesday we have our match in the Champions League that will give us the opportunity to redeem ourselves and get going again" he told reporters.
"At the moment we're playing a bit in bursts, so we should look to play with a bit more conviction, otherwise it all becomes more difficult," added Allegri.
"On Tuesday we have to play a different game, not technically, but we have to have more conviction and believe in ourselves."
Palermo took the lead in the 41st minute against Cagliari when Uruguay midfielder Arevalo Rios opened his account for the season with a deflected shot from the edge of the area after Fabrizio Miccoli cut the ball back through a crowd of players.
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