Juve went ahead after three minutes when Argentine Higuain curled a shot into the net after slaloming through the defence.
Atalanta's Alejandro Gomez then had a penalty saved by goalkeeper Gianluigi Buffon, who was back after a two-month injury layoff, in the 25th minute after a handball.
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Higuain had the chance to make it 2-0 for the visitors but volleyed just over the bar shortly before Juventus midfielder Blaise Matuidi missed the target with a fine curled shot.
Buffon shone again when he denied second-half substitute Andrea Petagna three minutes from time to elave Juve in the driving seat ahead of the second leg.
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