Goals from Mario Yepes, M'Baye Niang and Giampaolo Pazzini sealed a comfortable win for the hosts and paved the way for a mouthwatering quarter-final with the Italian champions
After labouring to break down the visitors in the first half, a powerful header from Mario Yepes and a quick-fire double from M'Baye Niang and Giampaolo Pazzini saw the Rossoneri cruise to victory, and set up a tantalising tie with Juventus in the next round.
The hosts bossed the opening exchanges and carved out the first real opening after 15 minutes when Pazzini was played in behind behind by Robinho only to see his effort blocked by the onrushing Davide Facchin.
Reggina struggled to get out of their own half in the first quarter of the game, but Manuel Fishnaller should have done better after turning well to work space for a shot on the edge of the area. Instead, though, he blazed over.
The visitors thought they had taken a shock lead shortly before the 25-minute mark, but Dario Bergamelli's well-taken finish was correctly ruled out for offside following a deep free kick. Bojan Krkic's header was then parried by Facchin just a minute later to keep the scores level.
Milan continued to press for the opener but, despite dominating possession, they found it difficult to find a way through the visiting defence and its three-man shield in the centre of midfield, with Pazzini's header straight into Facchin's arms indicative of their struggle for inspiration in the final third.
The hosts came out of the blocks quickly after half-time and almost found an opening when Ignazio Abate prodded through towards Robinho, but the Brazilian could not quite reach the pass and Facchin gathered.
But the Rossoneri did not have to wait much longer for the breakthrough. After Robinho's header was brilliantly blocked on the line after Emanuelson's corner, the Brazilian returned the ball out wide to the Dutchman and his excellent cross was powerfully headed home by Yepes.
With the deadlock broken, Massimo Allegri opted to give youngster Niang a chance to impress and he almost scored with his first involvement, after controlling Pazzini's pass but Facchin was alert to smother the danger. Emanuelson then forced his way through a number of challenges only to be denied by the Reggina stopper once more.
Facchin was the busiest man on the pitch by this point, saving well from Abate's shot across goal after some good interplay with Niang and Pazzini, before making a superb one-handed stop following Pazzini's instinctive effort on the turn.
Reggina responded by finally pushing men further forward, but the tie was settled with two strikes in quick succession. First, Niang doubled his side's lead by slotting coolly past Facchin following Emanuelson's run and pass, before Pazzini was finally rewarded for his efforts when he turned inside the box and fired high into the corner of the net.
Reggina attempted to rally but Allegri's side ultimately cruised the final exchanges to progress to the next round, where they will face table-toppers Juventus.