The home team scored twice in the first half with goals from Timothy Castagne and Duvan Zapata.
Colombian striker Zapata claimed his second in the 86th minute his 17th goal in his last 10 games to set up a semi-final against Fiorentina.
Juve have won four Coppa Italia titles under manager Massimiliano Allegri.
Atalanta took the lead through Castagne goal as he coolly slotted a shot into the bottom corner.
Just two minutes later, Zapata punished Juve for failing to clear the ball as it pinged around the box, rifling a shot past goalkeeper Wojciech Szczesny.
The Serie A leaders, who are unbeaten in the league, had chances in the second half and came close with a Sami Khedira volley but he was denied by a good save from Etrit Berisha.
Zapata then pounced on a poor Mattia de Sciglio back-pass for the third goal in the closing stages.
Fiorentina beat Roma 7-1 in their quarter-final as Federico Chiesa scored a hat-trick and AS striker Edin Dzeko was sent off for arguing with the referee.
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