Inter scored twice in the space of three minutes.
Edin Dzeko scored a direct shot from close range in the 8th minute, before Henrikh Mkhitaryan doubled the lead, taking advantage of a cross from Federico Dimarco in the 11th minute.
Hosts Milan appeared in a state of shock and had no first-half attempts.
Milan improved in the second half but failed to create any real chances.
And attempts from Brahim Diaz and Junior Messias missed the goal, while Sandro Tonali’s attempt hit the post.
Note that the return match between the two teams will take place next Tuesday.
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