Two maiden San Siro goals from Suso had put Milan on course to reach second place in the Serie A table but, with Antonio Candreva having pulled a goal back 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.
As important to the fans as the game itself are the large-scale banners - or choreography - displayed in rival stands before kick-off.
Milan Ultras paid tribute to departing owner Silvio Berlusconi, the former Italian Prime Minister whose era witnessed eight Serie A titles and five European Cups. The north stand simply hailed Inter as 'the most beautiful' - a show of faith from a set of supporters who have had little to admire in recent years.
Their heroes started the brighter, with Mauro Icardi directing Joao Mario's cross into Perisic's path for the Croatia international to get Milan's teenage goalkeeper Gianluigi Donnarumma working.
Perisic's powerful header on Danilo D'Ambrosio's assist fizzed over the bar and, in the 26th minute, Geoffrey Kondogbia rose highest to nod wide at a corner.
Inter's midfield lost some bite when Gary Medel, known as 'The Pitbull', was withdrawn hurt. Ball-playing defender Jeison Murillo replaced him.
Mattia De Sciglio fired Milan's first warning as Inter's enthusiasm began to wane and the Nerazzurri were soon properly punished for easing off.
Against the run of play, at the end of a counter-attack orchestrated by Giacomo Bonaventura, Suso cut inside from the right to beat Samir Handanovic to his far post.
When play resumed Milan pushed hard for a second goal to really knock Inter's resolve and Bonaventura was unlucky to come up against the covering D'Ambrosio when he burst into the box.
Inter were not cowed, though, and Candreva promptly dragged them back into the contest with a screamer from 25 yards while Milan's players contested the awarding of a throw-in.
The celebrations lasted five minutes. Carlos Bacca and Suso combined to sit Miranda down and, with a precise daisy-cutter, Suso beat Handanovic.
Inter needed to hit back quickly or risk running out of energy against a team well-equipped to shut up shop, and Candreva did well to pick out Perisic for a shot on the turn that screeched past a post.
Icardi, the captain who fell out with Inter fans this autumn, missed a chance to redeem himself when sticking the ball wide from a one-on-one with the 17-year-old Donnarumma.
With time running out the ever-impressive Perisic ploughed down the left wing to set up Icardi for another run at the young Milan keeper, who covered skilfully.
Perisic took matters into his own hands two minutes into stoppage-time. When Murillo's header put the ball on a plate in the Milan box, Perisic slammed it into an empty net with his left boot.
