Since drawing at Juventus 0-0 at Juventus on December 9, Inter have failed to win their last four games, a winless streak that has seen them fall from first place to third place in Serie A and out of the cup.
Milan had the first real chance after 18 minutes, as Giacomo Bonaventura’s towering header was fingertipped over the bar by Samir Handanovic.
Inter thought they had taken the lead in bizarre circumstances, as Ivan Perisic knocked back a corner from the by-line and Antonio Donnarumma knocked it into his own net at the near post, but VAR confirmed Andrea Ranocchia was offside and standing practically on the line.
Handanovic again got down to beat away a Suso angled drive following Franck Kessie’s back-heel flick, while Perisic wanted a penalty, but Leonardo Bonucci’s arm was flush against his torso.
A Bonucci error sent Joao Mario into the box, but Ignazio Abate sprinted back to block, then Mauro Icardi’s backwards header flew inches past the far top corner.
Lucas Biglia blasted off target when unmarked on the edge of the box from a corner. Abate went off with another muscular injury and Donnarumma came tearing off his line to clear from Icardi.
Joao Mario should’ve scored on the hour mark when Icardi knocked down a cross for the Portugal international, but he fired it straight at Antonio Donnarumma from point-blank range for a sensational reaction save.
Matias Vecino had a pop from a huge distance and Suso hit the side-netting, but when Handanovic flapped a Suso cross into the path of Bonaventura six yards out, his diving header was incredibly over the bar.
Joao Mario was jeered off the field after another below-par performance and Kalinic was carried off with an ankle injury, replaced by Patrick Cutrone.
Suso’s curling cross-shot took a deflection off Milan Skriniar to bounce off the top of the crossbar, then at the other end Bonucci’s desperate sliding block did enough to force Perisic to blast over.
Donnarumma did well at the 87th minute to parry first Perisic’s strike, then the Candreva follow-up from close range. Suso’s attempt was deflected inches wide with Handanovic wrong-footed.
It went to extra time, the fourth of Inter’s last five Coppa Italia ties to have gone beyond 90 minutes. The Rossoneri were more aggressive, with a series of dangerous crosses and corners.
It paid off, as Suso chipped a ball over the top, substitute Patrick Cutrone sprung the offside trap and kept his cool to sweep the finish past Handanovic from 10 yards. The teenager was booked for taking his shirt off during wild celebrations.