In an utterly breathless opening half, Juve - targeting a Serie A and Europa League double this season - set about their opponents like a team possessed in Thursday's second leg and would have been out of sight but for the heroics of goalkeeper Onur Kivrak.
But Kivrak could do nothing to prevent Arturo Vidal's 17th goal of the season after 19 minutes and Pablo Daniel Osvaldo capped a fine display in Turkey by heading in from close range just after the half hour to confirm a convincing aggregate win.
It leaves the Italian champions on course for the dream final at their home ground, although first up are Serie A rivals Fiorentina, who inflicted Juve's only league defeat of the campaign when the sides met earlier this season.
Although Antonio Conte changed his forward line from Sunday's Torino victory, Juventus started strongly and almost went in front when Sebastian Giovinco fed Mauricio Isla in oceans of space on the right, but his shot was superbly tipped onto the post by Kivrak.
Despite having the luxury of a two-goal cushion from the first leg, there was no let-up from Juve and Kivrak again kept his side in it by thwarting Leonardo Bonucci and then producing a fabulous reflex save from Isla's powerful 18-yard effort.
Juve finally got the goal their determined start deserved after 17 minutes. Giovinco played a neat one-two with Osvaldo, whose cross found the Italian 10 yards out. Giovinco's first-time shot produced an amazing point-blank save from Kivrak before Vidal smashed home the rebound.
Conte's men were rampant and doubled their advantage on the night after 33 minutes when Giovinco latched on to an inch-perfect pass before crossing for the unmarked Osvaldo to head home.
Such was the dominance of the away side that Conte was able to withdraw Pogba before half-time to rest the Frenchman for Sunday's trip to Milan.
The unrelenting pace of Juve's first-half performance subsided after the restart, but they still looked dangerous and the magnificent Giovinco's delicate effort had Kivrak beaten, but Aykut Demir got back to head clear.
Both players really caught the eye and it was Osvaldo's turn to go close moments later when his quick footwork gave him space for a shot in the area before he lashed over.
Juve substitute Simone Padoin almost added a third late on, but Kivrak scrambled clear.
