The Argentine headed home in the opening minutes of the city clash and, despite being reduced to 10-men, the away team held on to defeat their arch-rivals and record a vital win
The Argentine headed home from Esteban Cambiasso's cross with one of the first attacks of the match, and Andrea Stramaccioni's charges shrugged off the sending off of Yuto Nagatomo to keep their rivals at bay and take all three points.
Needing a victory to move within four points of Serie A leaders Juventus, Inter could not have asked for a better start.
Barely four minutes were on the clock when Cambiasso's free-kick eluded Christian Abbiati, who had come out rashly.
Samuel was waiting at the far post, and did very well from an acute angle to steer the ball into the open net and put his team into the lead.
Compatriot Diego Milito could have doubled the advantage moments later, but failed to capitalise on Abbiati's poor clearance and was denied twice by the goalkeeper.
Struggling to create openings with just Bojan as a solitary forward, Milan looked most likely to create something from distance.
Riccardo Montolivo sent Samir Handanovic sprawling with a venomous long-range effort, but the midfielder sent his shot inches wide of the post. Kevin-Prince Boateng also had the chance when the visitors were robbed in defence, but the Ghanaian failed to hit the target and squandered a great opportunity for Milan.
As the first-half was coming to a close the Rossoneri thought they had drawn level. Handanovic's punch landed squarely at the feet of Montolivo, who this time powered the ball into the net. Celebrations were short-lived, however, as play was brought back for a marginal foul on the goalkeeper after clearing the ball.
Bojan was also denied by the shot-stopper in the period's closing stages, meaning that Inter went into the break with a slender lead.
The visitors' task was made more difficult just after the restart when Nagatomo was sent off, reducing the away team to 10 men.
The Japan international had been booked in the first-half and, although his handball in the middle of the pitch seemed innocuous enough, referee Valeri had no hesitation in showing the Inter man his second yellow to the disgust of coach Andrea Stramaccioni.
Massimiliano Allegri introduced both Ignazio Abate and Robinho into the action to try and take advantage of the numerical superiority, but despite enjoying extended periods of possession Milan had few clear-cut openings to force their way back into proceedings.
A couple of chances by Montolivo from distance failed to test Handanovic, while Bojan also fired wide. Another Montolivo thunderbolt then forced Handanovic to parry, and Boateng spurned his chance on the volley when he had time to control the ball in the area.
Bojan was the next man to fluff his lines when Montolivo presented the opening. The former Barcelona man was onside when the midfielder once more blasted the ball from deep, but having collected the rebound he slipped at the last moment and allowed Handanovic to recover.
Inter hearts were once again in their mouths 15 minutes from the end when Robinho's well-placed cross looked destined to end at the feet of Giampaolo Pazzini. The striker threw himself at the ball, but failed to connect at full stretch and the Nerazzuri started again with a goal kick.
Milan threw everything at the visitors in the final moments, but Inter held firm and, thanks to the flawless keeping of Handanovic, were left to celebrate victory.
The win moves the club onto 15 points from their opening seven games, level in third place with Lazio. Milan, meanwhile, remain in mid-table obscurity having been condemned to their fourth defeat in seven.