Simone Inzaghi's side won the Supercoppa Italiana in midweek with almost the last kick of the game, but there was no such drama at the Gewiss Stadium as the visitor missed the chance to extend its lead at the top of the table.
Edin Dzeko was guilty of a glaring miss in the second half, with Inter failing to score in a league game for the first time this season.
The result means Inter remains top – two points clear of bitter rivals Milan – while Atalanta stays fourth, one point ahead of Juventus.
Inter dominated possession in the early stages, but did not threaten the Atalanta goal until the 26th minute when Juan Musso superbly pawed away Alexis Sanchez's powerful strike.
Atalanta had to wait until the 39th minute for their first effort on target, Matteo Pessina's header comfortably kept out by Samir Handanovic.
The Inter goalkeeper denied Pessina again soon after the interval, racing off his line to thwart the forward after an incisive move from the hosts.
Dzeko's attempt was repelled by Musso at the other end and the 35-year-old inexplicably headed over from four yards with 20 minutes remaining.
Handanovic superbly denied Luis Muriel in the 80th minute after Alessandro Bastoni had been caught out, while Danilo D'Ambrosio squandered the opportunity to seal all three points for the visitors late on when he fired into the side netting with only Musso to beat