Kevin Trapp had been Frankfurt's hero with his penalty save in the goalless first leg and, without a recognised striker to call on, Luciano Spalletti's Inter side were toothless throughout Friday's (AEDT) meeting.
Jovic showed Inter – still without Mauro Icardi, who has not played since being stripped of the captaincy in mid-February – what it was missing with a composed finish that paved the way for a dominant Frankfurt display at San Siro.
Sebastien Haller hit the woodwork prior to Jovic's strike and Frankfurt would have had more if not for fine work from Samir Handanovic and Milan Skriniar as Inter, which faces AC Milan in a huge Serie A clash on Monday (AEDT), went out with a whimper.
Any doubts over Frankfurt's approach to the contest were put aside after four minutes – Haller hitting the crossbar after Handanovic had kept out Mijat Gacinovic's effort.
Inter failed to heed that warning, though, and Frankfurt had the lead a minute later when Jovic capitalised on Stefan de Vrij's misjudgement and lofted a delicate finish over Handanovic.
Haller looked to have made it 2-0 before the half hour, but the offside flag came to Inter's rescue before the striker and Gacinovic were denied in the same move by Handanovic's superb double save.
Jovic could have doubled his tally after the restart, only to slip at the vital moment, while Skriniar made a crucial challenge to deny Gacinovic a free shot at goal.
But, despite Jovic heading straight at Handanovic late on, Frankfurt was not made to pay for its profligacy, speculative efforts from Antonio Candreva and Skriniar the most Inter could muster as its European hopes were limply extinguished.