The Argentina striker sealed a pulsating clash after Ricardo Rodriguez impeded Danilo D'Ambrosio on a corner late, having twice given Luciano Spalletti's side the lead with wonderfully taken goals.
Suso netted impressively for Milan's first equaliser and Samir Handanovic's own-goal nine minutes from time had a third consecutive 2-2 draw in this fixture on the cards before Icardi had the final word.
"Taking home the match ball is a special feeling, I can't describe it," he told Mediaset Premium.
"I had spoken to some of my team-mates and knew I had to score today, so I am holding on tight to this ball."
Icardi now has 87 in Inter colours but has endured an often tempestuous relationship with supporters during his San Siro career and was without a goal from open play since August's 3-1 win at Roma.
"I let the critics talk, then I do what I have to do on the pitch: I help the team and score goals," he said.
"You can't always score, of course. I am happy for me and for Inter, above all for this victory."
Seven wins and a solitary draw from eight games under Spalletti means Inter are only two points shy of Napoli at the top of the table, and Maurizio Sarri's men must defend their 100 per cent record when they host the Nerazzurri in a mouth-watering clash on Saturday.
"It's too early to talk about a Scudetto challenge," Icardi added. "We are doing things the right way from pre-season and now we have to think about the next match against a great opponent like Napoli.
"It's a special match because they are the leaders and play the best football in Europe."