Vlahovic signed for Juventus from the Fiorentina during the winter transfer and has been decisive in both his first two matches, opening the scoring against Verona on Sunday and ramming an 88th-minute shot against Ruan Tressoldi and past Sassuolo's veteran goalkeeper Gianluca Pegolo.
The Serbia forward broke the deadlock generated by Paulo Dybala's third minute opener and Hamed Traore's delightful individual effort midway through the first half, just as the match looked to be heading to extra-time.
Up to that point Pegolo, who is 40, had done his best to keep Juve at bay, with his fingertip save of Adrien Rabiot's glancing header with eight minutes remaining the highlight of a fine performance.
However the hosts were also unlucky, with Weston McKennie striking the post with a curling effort and then forcing a save from Pegolo in the match's most chaotic moment.
Matthijs de Ligt smashed the rebound against the post before Sassuolo's Gian Marco Ferrari thumped the ball against Leonardo Bonucci and over the bar.
However with the clock ticking Vlahovic bustled his way past Mert Muldur and forced the unfortunate Tressoldi's own goal which gives Fiorentina an opportunity for revenge on their ex-striker.
They are in the last four thanks to Vlahovic's compatriot Nikola Milenkovic, who fired Fiorentina into the last four with the last kick of a 3-2 win at Atalanta.
Milenkovic beautifully cushioned a knock-down and arrowed a low finish past Juan Musso in the fourth minute of added time.
Atalanta looked to be heading for the semis when Davide Zappacosta and Jeremie Boga cancelled out Krzysztof Piatek's ninth-minute penalty.
But Pole Piatek levelled the scores with 19 minutes remaining on the rebound after fluffing another spot-kick.
Despite Viola defender Lucas Martinez being sent off for two bookable offences eight minutes after Piatek netted his second, Milenkovic then lashed the away side ahead in the very final moments.
And after an agonising VAR check for an offside in the build-up referee Michael Fabbri awarded the goal and immediately blew to ensure Fiorentina's passage into the semis.