MILAN, Aug 24 (Reuters) - Inter Milan beat AS Roma 6-5 on penalties to win the Italian Super Cup on Sunday following a 2-2 draw in Jose Mourinho's first competitive game in charge of the Italian champions. Sulley Muntari, a new signing from Portsmouth, gave Inter the lead after 18 minutes of his official debut after Maicon's cross had been deflected on to the bar by Roma defender Philippe Mexes. Last season's Cup winners Roma, playing their first game since the death of club president Franco Sensi last Sunday, levelled on 59 minutes at the San Siro when Daniele De Rossi lashed a stunning drive into the top corner from 30 metres. Inter substitute Mario Balotelli thought he had snatched victory with a cool finish on 83 minutes but Roma forced a second equaliser in the final minute of normal time when the ball seemed to come off Mirko Vucinic and Inter's Dejan Stankovic. After a dull extra time, Juan missed the crucial spot kick in the shootout to give Inter victory before they start the defence of their Serie A title at Sampdoria next Saturday. Former Chelsea boss Mourinho, appointed in June after Roberto Mancini was sacked despite winning the title, was forced to play midfielder Esteban Cambiasso in defence because of injury problems but his side still dominated at times. 'I've won the Super Cup... but I want to remember that I've won it because Roberto Mancini won the last championship,' a gracious Mourinho told reporters. 'This game is a reply to those who say they don't play good football in Italy. We've seen four goals and a spectacle.' CONSTANTLY BOOED Inter winger Mancini, signed from Roma in the close season, was constantly booed by the small contingent of away fans but put in a decent performance on the left of Mourinho's favoured three-pronged attack with Luis Figo on the right. Zlatan Ibrahimovic played as the lone front man despite nagging knee trouble and he went very close to scoring before Ghanaian Muntari struck. Luciano Spalletti's Roma, who handed competitive debuts to Julio Baptista and John Arne Riise, improved after the break in the season's curtain-raiser and deserved their two equalisers. Roma, who beat Inter 1-0 in last season's Super Cup, were ahead in the shootout after Stankovic hit the bar but Francesco Totti struck the woodwork and Juan's effort was saved by Julio Cesar before captain Javier Zanetti sealed Inter's win.