Two maiden San Siro goals from Spanish schemer Suso had put Milan on a course to reach second place in the Serie A table.
However, with Antonio Candreva having grabbed Inter’s first leveller at the start of the second half, Perisic put the brakes on the Rossoneri.
The point will mean a lot to new Inter head coach Stefano Pioli, hired to fix the mess left behind by Frank de Boer, who departed with the Nerazzurri languishing in the bottom half of the table.
Former Liverpool man Suso put Milan ahead in the 42 minute with a brilliant left-footed shot that beat Samir Handanovic all ends up.
Just eight minutes after the restart, Candreva fired home an excellent fierce right-footed shot that found the top right corner, leaving Gianluigi Donnarumma with no chance.
In the 58th minute, Suso then doubled his tally with a neat right-footed finish that was placed well into the bottom left corner.
Milan looked on course for an important victory but with the game almost up, Perisic tapped home to earn a point for Inter, who sit ninth in Serie A.
Milan, who sit third in Serie A after the 2-2 draw, face Empoli away next on Saturday, November 26.
Meanwhile, Inter, buoyed by the late equaliser, travel to Hapoel Be’er Sheva in the Europa League on Thursday, November 24.