Second-placed Milan slipped five points behind Inter when forward Fabrizio Miccoli scored one goal and helped set up Mark Bresciano for the second in mid-table Palermo's deserved win.
Miccoli cut inside and arrowed in an unstoppable drive early in the second half before producing great skill on the flank to allow Australian Bresciano to slam the ball into the net.
"We knew we could do well today. We thoroughly deserved it. We are a good team, today we showed it," Miccoli told Sky TV.
Simone Tiribocchi equalised for struggling Atalanta nine minutes from time after Lucio failed to stop a through ball but Inter's Thiago Motta could still have won it in stoppage time.
"Maybe it's an opportunity missed by the others but not by us," Inter assistant coach Beppe Baresi said.
"It's the only foul he has done in recent games," he added, referring to Sneijder's second yellow card.
Inter coach Jose Mourinho, who like counterpart Antonio Conte was in the stands after being sent off in last weekend's defeat at Juventus, avoided the media after the game but still managed to get into a spat with a journalist by the team bus.
REDEEMED HIMSELF
Genoa are among five clubs a point further back after losing 1-0 at Lazio, who recorded only their third league win of the campaign thanks to wingback Aleksandar Kolarov's classy goal.
Catania dropped to bottom in Sinisa Mihajlovic's first game in charge after a 1-0 home defeat by Livorno and Siena's 2-1 victory over Udinese, their second win in a row.
