Paulo Dybala's stunning volley put the Serie A leaders in front after 22 minutes at Juventus Stadium, and he played in Mario Mandzukic for the home side's second 12 minutes later.
Gian Piero Gasperini's spirited Atalanta side rallied late in the game with goals from substitutes Abdoulay Konko and Emmanuel Latte Lath, but Miralem Pjanic's penalty booked Massimiliano Allegri's men a clash with either Milan or Torino in the quarter-finals.
Atalanta have been the surprise package of Serie A this season and they arrived in Turin hoping to improve on the 3-1 league defeat they suffered at the same ground in December.
But they came up against a supremely confident Juventus attack despite Allegri's decision to rest star striker Gonzalo Higuain, and the Bianconeri hung on for the win at the end.
Atalanta's Alberto Grassi tested Juventus goalkeeper Neto with a low drive in the opening 30 seconds of a lively start to the match as the Serie A champions went toe-to-toe with one of this season's brightest teams.
Juve steadied themselves and should have taken the lead when Stephan Lichtsteiner's cross found Mandzukic unmarked, but the ball hit the Croatian striker's body before striking the post on its way wide.
The visitors' bright start seemed to work against them as a galvanised Juventus poured forward, and the opening goal was a delight to watch as Mandzukic headed a cross back to Dybala, who struck the sweetest of volleys to leave goalkeeper Etrit Berisha with no chance.
There was no let up from Juve's front pair and after 33 minutes Dybala played Mandzukic into the area and the 30-year-old side-footed his sixth goal of the season in at the far post, before missing a golden chance to make it 3-0 just before half-time.
Atalanta made a more cautious start to the second half than they had the first, but even sitting deep they struggled to contain the tireless Juventus attack.
Sloppy play at the back by Konko allowed Stefano Sturaro to cross for Mandzukic, whose header looped dangerously back across the face of goal before Andrea Masiello acrobatically cleared the danger.
With a trip to Fiorentina awaiting his side at the weekend, Allegri replaced Dybala with Marko Pjaca after an hour and moments later Tomas Rincon, making his full Juventus debut, was denied his first goal for the club when Berisha tipped his rising shot over the crossbar.
Atalanta's travelling support were finally given something to cheer when Andrea Petagna squared the ball to Konko and the full-back hit an instinctive half-volley that bounced in off the post.
Juventus' two-goal lead was restored just three minutes later when Marco D'Alessandro tripped Lichtsteiner in the box and Pjanic made no mistake from the penalty spot, but Atalanta hit back again to ensure a tense finish to the game.
Andrea Conti got in behind the Juventus defence and crossed for Latte Lath to nip in ahead of his marker and squeeze the ball between Neto and the post, but there was to be no dramatic equaliser for Gasperini's men.