The result extended Inter's unbeaten start to the season and tied them at the top with Torino, who beat Venezia 1-0 earlier in the day. Both teams have seven points from three games.
Inter started the match in devastating style with two goals in the first 10 minutes.
The opener was a disaster for Atalanta defender Berat Djimsiti. He stretched to stop Thuram's cross but succeeded only in deflecting the ball past his own goalkeeper.
There was no luck about the second seven minutes later. Nicolò Barella volleyed home a cracker from the edge of the box to give Inter a commanding early lead.
Thuram hit the woodwork before half-time but he deservedly got his name on the scoresheet two minutes into the second half when he seized on a loose ball in the box and poked it home.
Nine minutes later, he got his second with another opportunist goal inside the penalty area.
Earlier, Saul Coco scored with five minutes remaining to give Torino a 1-0 win at Venezia and extend their unbeaten start to the season.
Coco's glancing header came at the end of a tepid game in which neither side created many clear-cut chances.
It was the central defender's first Serie A goal since joining Torino from Las Palmas this summer.
Venezia have one point from their first three matches and are second to last on the table. Atalanta are eighth.
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