0110 GMT January 18, 2020
Luciano Spalletti's team remained unbeaten this season and moved above champion Juventus up to second in the Serie A table but nerazzurri were made to fight hard by their neighbor after half-time at San Siro, goal.com reported.
Icardi's instinctive finish from Antonio Candreva's pinpoint 28th-minute cross preceded a passage of play before the interval when a Milan side still bedding in after its frantic close season in the transfer market appeared increasingly overmatched.
But Vincenzo Montella's decision to bring teenage forward Patrick Cutrone on for Franck Kessie at the break proved inspired and the Rossoneri were level when Suso stylishly picked out the bottom corner from long range.
Inter unexpectedly found itself on the ropes and was indebted to Samir Handanovic's stunning reaction save from Giacomo Bonaventura before Icardi started and ended a 63rd-minute counter-attack, crowning it with a brilliant volley.
Milan's head coach is likely to face more speculation over his future after a fourth defeat in eight Serie A matches but his team's spirit could not be called into question in the 81st minute when Bonaventura turned the tables on Handanovic – the goalkeeper fumbling over the line to be credited with the own goal.
There would be a further twist when Ricardo Rodriguez was adjudged to have impeded Danilo D'Ambrosio at a corner and the Argentina striker proved to be the coolest man in a stadium ramped up to fever pitch.
Match-winner Icardi was planning to keep the match ball close at hand after scoring a derby hat trick.
Icardi told the club's official website, "I do not know if I will sleep with the hat-trick ball – I usually do not sleep after matches – but I will keep it close because it is a special ball.
"A hat-trick in a derby is a special thing.''
However, no one within the Inter camp was getting carried away as manager Luciano Spalletti attempts to stamp his mark on the team.
Icardi said, "We are still at the beginning and we still have a lot to do. We are happy to be where we are – that means we are doing things well.''
Milan boss Vincenzo Montella was perhaps understandably unhappy with the penalty decision.
He told La Gazzetta dello Sport, "Ricardo did not pull him down. He was very skilled, D'Ambrosio, and it makes me angry to lose in this way. I hope for a penalty like this in the next games.''
Milan currently sits in 10th place in the table, but Montella is confident things are starting to turn.
He said, "I'm proud of what the team has pulled out. We reacted with pride and showed Milan's soul.
"The effort has not been rewarded, but I'm very optimistic and even tonight, the glass is half full. I see a team that goes ahead with a precise game principle.''