Eintracht, losing finalists last year, will get their chance for silverware again when they take on overwhelming favourites Bayern, 6-2 winners against Bayer Leverkusen on Tuesday, in the final in Berlin on May 19.
The 20-year-old Jovic stabbed in from a corner against the run of play to set up an extraordinary final clash for Kovac.
The Croat this week signed a three-year contract at Bayern from next season, leaving Frankfurt angry with the Bundesliga champions over the poaching of their coach, who has turned them from relegation candidates into European hopefuls this season.
"We are here, we are in the final now and we can all be happy. Everyone who is associated with the club," Kovac, who used a special clause to get out of his Eintracht contract to sign with Bayern, told reporters.
"Of course, I want to win the final. We wanted it last year (against Borussia Dortmund). This year it is a different team but, again, a top team."
The game at Schalke lacked the fireworks of Bayern's semi-final and needed more than an hour to catch light with the hosts having the far better chances.
Guido Burgstaller twice came close and forced a few superb saves from Lukas Hradecky but they could not convert any of them before their opponents struck from a set piece.
Eintracht were left with 10 men in the 81st minute when substitute Gelson Ferdandes, who had only been on the pitch for 33 seconds, was shown a straight red card for a rough challenge on Leon Goretzka.
Schalke tried desperately to find an equaliser and actually had the ball in the net deep into stoppage time only for the referee to rule it out for handball.
(Reporting by Karolos Grohmann; Editing by Ian Chadband)
