Serbia forward Jović doubled his goal tally for the season, with Tijjani Reijnders sealing the tie late on, as Milan fans were given something to shout about in what has been an awful season for the seven-time European champions.
Milan are unbeaten in all five of this season’s local derbies, winning the Super Cup final against Inter in January, and Wednesday’s win also ended Inter’s hopes of repeating the Serie A, Champions League and cup treble won under Jose Mourinho in 2010.
“Jović is working really hard, in particular in the last three or four weeks. He’s lost a bit of weight too, which helps,” said coach Sérgio Conceição.
“He gives us something that we needed for this match, every forward has their own set of qualities. He doesn’t give defenders a lot to work with,” he added.
Conceição’s side, who sit ninth in Serie A and will almost certainly miss out on Champions League football next season, will likely face Bologna in next month’s final in Rome.
Bologna lead Empoli 3-0 ahead of their second leg on Thursday and are set to reach a major tournament final for the first time since last winning the cup in 1974.
“We’re happy to be in the final, but we haven’t won it yet,” added Conceição. “I’m not a different coach to the one from a couple of days ago, and the players aren’t any different either. It’s not like everything is great now, just like it wasn’t all bad before.”
Given a rare start, Jović put Milan ahead on the night and in the tie in the 38th minute when he met Alex Jimenez’s cross with a thumping header, the nominal away side’s first chance of the game.
Federico Dimarco had hit the bar and Lautaro Martínez smashed a great chance over before Jović opened the scoring, and the 27-year-old extended Milan’s aggregate lead three minutes after the break.
Jović pounced to poke home from close range after Inter failed to deal with a basic corner, sparking four immediate substitutions from Inter coach Simone Inzaghi which came to nothing.
Instead Reijnders completed a comprehensive win for Milan five minutes from the end when he rolled home with a first-time finish after being slipped in by Rafael Leao.
Elimination at the hands of their local rivals is a big blow to Inter who had genuine ambitions of the treble after booking a Champions League semi-final against Barcelona last week.
But Inter are also level on points with Napoli at the top of Serie A after losing to Bologna at the weekend and could easily end an excellent season empty handed.
Inzaghi’s players have a packed and challenging run-in with Champions League chasers Roma visiting the San Siro on Sunday before the first leg of their last-four clash with Barcelona which could yet make or break their campaign. (AFP)
