They blitzed their way into a quick-fire lead with two goals in the first 11 minutes and could easily have put the tie to bed after a dominant first-half display.
Milan improved after the break but will be grateful to still be in reach of the 2010 champions after a disappointing performance in front of their supporters.
The fierce rivals had not met in the Champions League since a quarter-final clash in 2005, which was abandoned after 73 minutes of the second leg when a section of Inter fans hurled flares on to the pitch – one of which struck and injured Milan goalkeeper Dida.
Milan, bidding for an eighth European Cup trophy and a first final since their 2007 success, were dealt a blow before kick-off with star forward Rafael Leao ruled out by a muscle injury and they were soon blown away by a blistering start from Simone Inzaghi’s side.
Inter were ahead after just eight minutes as former Manchester City striker Edin Dzeko outmuscled Davide Calabria from Federico Dimarco’s corner and thrashed a volley from 12 yards past the helpless Mike Maignan in the Milan goal.
One foot in the final: Inter enjoyed a brilliant night against their rivals
/ AFP via Getty ImagesAnd they had a second just three minutes later. Dimarco was released down the left and cut the ball across the box into the path of the onrushing Henrikh Mkhitaryan, who marched through the Milan defence to stroke past Maignan.
The Rossoneri were all at sea and Inter came within inches of a third when former Milan midfielder Hakan Calhanoglu lashed a 25-yard strike against a post, before Maignan blocked Mkhitaryan’s effort from close range.
There was a huge moment of relief for Stefano Pioli’s side after Inter were awarded a penalty in the 31st minute as Lautaro Martinez went down under a challenge from Simon Kjaer. But Spanish referee Jesus Gil Manzano was asked to review his decision by the VAR and decided to overturn his original call.
Martinez flashed a strike narrowly over before Denzel Dumfries just failed to apply the finishing touch to Dimarco’s cross-shot as Inter continued their total dominance of the first half.
Milan started the second period much better. Brahim Diaz curled just wide from 20 yards and Junior Messias wasted a great chance when through on goal.
Dzeko was denied by a good one-on-one save from Maignan but Milan’s improvement continued and substitute Divock Origi played a key role in setting up Sandro Tonali, whose strike cannoned off the base of the left post.
But Inter drew the sting out of Milan’s revival and took a big step towards the final in Istanbul.
Additional reporting from PA
