Milito's strike in the 54th minute was enough to earn the designated visitors all three points at the San Siro and take them to within six points of the summit - and just five of their city rivals.
It was the Argentineans third goal in two matches following his brace against Parma last weekend and it also marks a return to form for the striker for had a forgettable 2011.
"I'm really happy, truly content," Milito told the club's website.
"We've played a great game against a great opponent.
"We knew that it would be difficult but we have played a game of great concentration.
"It was an important test for us, for our position in the table and for morale. We're very happy.
"To win a derby is the most beautiful thing, above all for the fans. Thanks to them, because they are always behind us. This goal is for them."
Inter were worthy winners for the result, winning the match even after they had a goal wrongly disallowed early on for offside.