Milan, looking to move up to second behind Juventus after Roma's 2-1 slip-up earlier at Atalanta, were seconds away from securing the local bragging rights.
Suso broke the deadlock on 43 minutes and hit a brilliant second before the hour after Antonio Candreva had given Stefano Pioli's men hope with a well-struck but controversial 53rd-minute leveller.
However Milan's celebration plans were promptly cancelled as Perisic, the Nerazzurri's star player on the night, coolly side-footed past teenaged goalkeeper Gianluigi Donnarumma from a knocked-on corner in the first minute of added time.
Milan remain third and level on points with Roma, with both seven points behind leaders Juve. Inter are up to ninth.
It was new Inter coach Pioli's first game in charge of a Serie A club since being sacked by Lazio following a 3-1 defeat to city rivals Roma in April.
The 51-year-old saw his team dominate an enthralling opening half that had Donnarumma on his toes only for Suso to fire Milan into the lead just before the break, and he wants improvements up front.
“To score goals you need determination and a little anger, this is certainly something we have to improve on,” Pioli said afterwards.
“We have to find players who have this kind of attitude.”
Although not a direct reference to Inter striker Mauro Icardi, who failed to add to his league-leading tally of 10 goals on the night, the Argentine has been warned.
He was one of several Inter players to spurn chances in a dominant first half in front of over 77,000 fans.
Perisic sent a flying header from Danilo D'Ambrosio's cross just wide with one of Inter's best chances in the opening period, before they suffered a blow when tough-tackling defender Gary Medel hobbled off to be replaced by Jeison Murillo.
Milan went in front shortly after, Giacomo Bonaventura holding the ball up on the edge of the area before setting up Suso for a superb curling shot that beat Samir Handanovic at his far post.
Milan threatened first after the restart, Bonaventura beating Geoffrey Kondogbia to see his drive deflected out by D'Ambrosio.
But minutes later the hosts were left furiously protesting a refereeing decision not to call a foul after Manuel Locatelli tumbled under a challenge on the left flank.
Inter's quick throw-in went straight to Candreva, who strolled across the edge of the area to beat Donnarumma with a superb shot into the top corner from 25 yards.
Milan coach Vincenzo Montella said later: “The referee had a great game tonight, but on that incident it was borderline.
“The ball did come off Locatelli but he was pushed into the ball and Inter took the thow-in quickly.”
But Inter's joy was short-lived.
Spaniard Suso played a one-two with Carlos Bacca and then produced some fancy footwork to get away from Joao Miranda before firing a shot past Handanovic and into the far bottom corner.
Yet Inter came fighting back and a great lob by Candreva set up Perisic for a left-footed first-time effort that inched wide of Donnarumma's far post.
Inter's persistance paid off as Milan made the mistake of leaving Croatian star Perisic with enough space to equalise.
“It's always disappointing when you concede so late in a game but the lads should be happy with their performance, their attitude and commitment was spot-on,” said Montella.
“They'll have a little trouble sleeping, but they shouldn't. We'd be a lot more disappointed if we had 10 points less.”