Unheralded Atalanta moved third in Serie A on Saturday with a 2-1 win over Genoa edging the side from Bergamo closer to a first-ever Champions League qualification with two games left this season.
Musa Barrow and Timothy Castagne's second-half goals sent Atalanta two points clear of Inter Milan, who play already-relegated Chievo on Sunday.
But AC Milan responded with Hakan Calhanoglu heading in the only goal against Fiorentina to keep Gennaro Gattuso's side's hopes of a return to elite European football since the 2013-2014 season alive.
AC Milan are fifth, one point behind Inter Milan, with Roma a further three points adrift in sixth before they host champions Juventus on Sunday.
"Today's win was really important, as the closer we get to the finish line, the more decisive each point becomes," said coach Gian Piero Gasperini.
"Mathematically, we have only a few points left to go, but it also puts us in a better state of mind going into the Coppa Italia final. The team has been extraordinary in terms of mentality."
Juventus and Napoli have already qualified for next season's Champions League, but behind them the scramble is frenetic in the chase for the two remaining berths.
Lazio beat Cagliari 2-1 in Sardinia on Saturday, to sit seventh in Serie A, five points adrift of Inter Milan and the top four.
Castagne and Duvan Zapata both had goals ruled out for offside in the first 20 minutes of the game, which was played at Sassuolo's Mapei Stadium because of work on Atalanta's home ground.
But 20-year-old Gambian Barrow broke through immediately after being substituted on at the break for his first goal this season, with Belgian Castagne adding a second on 53 minutes, finishing off Berat Djimsiti's low cross.
Goran Pandev pulled a goal back for Genoa one minute from time, but the fightback came too late as Atalanta extended their unbeaten run to 11 matches.
Atalanta's next two league games are against Juventus in Turin and back at the Mapei Stadium against Sassuolo on May 26.
The victory is a boost for Atalanta who head to Rome on Wednesday to play the Coppa Italia final against Lazio.
In Florence, French midfielder Tiemoue Bakayoko started for Milan despite his touchline bust up with Gattuso during last Monday's win over Bologna.
And the visitors broke through when Calhanoglu headed in Suso's cross after 35 minutes, condemning Fiorentina to their fourth consecutive defeat.
Napoli play at SPAL on Sunday after Carlo Ancelotti's side secured second place in the league last weekend.