Milito fires Inter to first-leg advantage
The Argentine, who has hit the net 13 times in Serie A this term since his move from Genoa, prodded in from close range after 34 minutes.
Mario Balotelli had set up his strike partner after outmuscling defender Cesare Natali but Fiorentina believed it was a foul and protested to the referee.
League leaders Inter, who beat Juventus in last week's quarter-final to prompt the sacking of Juve coach Ciro Ferrara, were not at their best at a half empty San Siro but Balotelli did have a header cleared off the line among other chances.
Fiorentina had opportunities too, most notably when Juan Vargas shot wide with only reserve goalkeeper Francesco Toldo to beat.
Kenya midfielder McDonald Mariga, signed from Parma on transfer deadline day on Monday, came on as a late Inter substitute for his first appearance.
The second leg takes place in Florence in April while in-form AS Roma host Udinese in the other semi-final first leg on Thursday.