It is the second time the San Siro rivals have drawn 2-2 this season, with Perisic rescuing an injury-time draw for Inter back in November.
Milan kept pressing, however, and were rewarded for their perseverance when central defender Alessio Romagnoli volleying home Suso's cross in the 83rd minute to set up a grandstand finish.
Inter looked nevertheless to be heading for a win that would have taken them up to sixth, one point ahead of Milan as both clubs fight for a Europa League place. A new era began at AC Milan on Thursday after the sale of Italy's most successful club to a Chinese-led consortium ended Silvio Berlusconi's 31 years in charge. Yonghong Li had claimed beforehand that Milan's new owners, just like the Suning Group, are primarily focused taking small steps on the road to recovery.
Inter appeared to be cruising after Antonio Candreva and Mauro Icardi scored to give them a 2-0 halftime lead before Alessandro Romagnoli pulled one back with seven minutes left.
A look at the Italian league table tells us that both the Milan giants are out of title contention and the title race is between Juventus and Roma, at this business end.
"Our first half hour was good, we created chances, but we weren't clinical enough".
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"Two weeks ago we were making other assessments, but we can only make those at the end of the season".
"In the second half there was a great reaction, a feat".
"In the first game I saw them cheer, this time I celebrated more than I usually do, I now understand the joy the Inter players felt in the first game".
Deulofeu went close again in the 14th but his effort went off the base of the right post from a tight angle.
The goal injected some freedom for Inter and they nearly doubled their lead moments later when Mario whipped in a low cross to the back post which just evaded captain Icardi. Ivan Perisic joined nicely with Joao Mario down the left and drilled a low cross to the path of Icardi, who fired to the gaping goal from six yards.
Little changed at the bottom of the table after Palermo picked up a point in a 0-0 draw with Bologna, Crotone held Torino 1-1, and Empoli earned a 1-1 draw at Fiorentina which maintained their four-point gap above the drop zone.