Dusan Vlahovic scored what proved to be the decisive goal in the fourth minute, racing through on goal before drilling the ball home.
The Serbia international thought he had doubled Juventus's advantage in the second half, but replays showed he had strayed into an offside position before heading beyond Marco Carnesecchi.
Atalanta forward Ademola Lookman threatened to net a late equaliser, only to see his powerful shot bounce off the woodwork.
Juventus ultimately stood firm to clinch a narrow win and their first major trophy since winning the Coppa Italia in 2020-21.
Meanwhile, Atalanta's 61-year wait for the Coppa Italia trophy will continue, but they will have the chance to end the season with silverware in next week's Europa League final against Bayer Leverkusen.
Vlahovic fires Juventus into an early lead
There has been plenty of speculation suggesting Juventus will part ways with Massimiliano Allegri at the end of the season, but all that talk was put on hold for Thursday's Coppa Italia final against Atalanta.
The Juventus boss saw his team get off to the perfect start, with Vlahovic breaking the deadlock inside the opening five minutes.
The Serbian striker latched onto Andrea Cambiaso's through pass, before firing past Carnesecchi to net his 18th goal of the season.
Vlahovic's early effort proved to be the first half's only shot on target as Atalanta struggled to break through a stubborn Juventus backline.
After being underwhelmed with his team's display, Gian Piero Gasperini turned to his bench at the break, introducing Mali striker El Bilal Toure.
Gasperini saw his troops make an encouraging start to the second period, with Ademola Lookman driving a deflected effort just wide of Mattia Perin's goal.
Atalanta fail to find elusive equaliser
As the contest entered the final 20 minutes, substitute Aleksei Miranchuk spurned a promising opportunity, lifting the ball harmlessly over the bar after meeting a low cross from the left flank.
Moments after Miranchuk blazed over, Vlahovic thought he had grabbed the all-important second goal, producing the deftest of headers from Cambiaso's inswinging delivery, only to see his goal chalked off for an offside infringement.
With the deficit still a slender one, Atalanta went agonisingly close to scoring the all-important equaliser when Lookman thundered a fierce strike against the upright.
After being saved by the woodwork, Juventus were then left frustrated as Fabio Miretti unleashed a fizzing strike against Carnesecchi's crossbar.
As it proved, Juventus did not require the insurance of a second goal as Perin made a strong save to deny Ederson in stoppage time, ensuring Vlahovic's early strike was enough to clinch their sixth Coppa Italia in nine years.
Meanwhile, Gasperini is left to reflect upon his third Coppa Italia defeat as Atalanta manager, leaving the experienced boss still searching for his first major piece of silverware.
The 66-year-old will hope his side can change that statistic when they face Bayer Leverkusen in next week's Europa League final in Dublin.