Two goals in a blistering opening half-hour were enough to seal an emphatic aggregate win for Antonio Conte's side.
In an utterly breathless opening half, Juve - targeting a Serie A and Europa League double this season - set about its opponent like a team possessed and would have been out of sight but for the heroics of goalkeeper Onur Kivrak.
But Kivrak could do nothing to prevent Vidal's 17th goal of the season after 19 minutes, and 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 is Serie A rival Fiorentina, which inflicted Juve's only league defeat of the campaign when the sides met earlier this season.
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.
The onslaught continued from the visitors with Claudio Marchisio and Paul Pogba both testing Kivrak from long range.
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.
Federico Peluso forced the rebound home, but was flagged offside.
Juve finally got the goal its 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 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 halftime to rest the Frenchman for Sunday's trip to AC Milan.
The unrelenting pace of Juve's first-half performance subsided after the restart, but the Italians still looked dangerous. The magnificent Giovinco's delicate effort had Kivrak beaten, but Aykut Demir got back to head clear.
Giovinco was denied again after 56 minutes when Osvaldo released the Italian in a lightning counterattack, but Kivrak stood tall and blocked the near-post effort.
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.
Trabzonspor was never in the game and was restricted to long-range opportunities, such as the one that Marc Janko blazed over just after the hour mark.
Juve substitute Simone Padoin almost added a third late on, but Kivrak scrambled clear.