Three-time winners Inter, who led 2-0 after the first leg, will face either Manchester City or Real Madrid in Istanbul on 10 June after a disciplined second-leg display ensured their progress.
Heavily backed at a feverish San Siro as the designated home team, Inter were made to absorb early pressure as a determined start by Milan ensured the match began at a frenetic pace.
Theo Hernandez fired marginally over with a ferocious strike and Brahim Diaz was denied by Andre Onana as Stefano Pioli’s side attempted to undo the damage done by conceding two goals inside 11 minutes last week.
The talented Rafael Leao, absent for Milan in the first leg because of a thigh injury, displayed flashes of inspiration on his return but shot agonisingly wide of the far post after driving in from the left.
Inter asserted themselves as the first half progressed and the tie would have been effectively over before the interval had it not been for Mike Maignan’s stunning reaction save from Edin Dzeko’s close-range header.
Inter had starved Milan of encouragement in a largely uneventful second half, before Martinez squeezed the ball under Maignan and into the bottom corner with 16 minutes remaining to send the Inter fans into raptures.
The full-time whistle was greeted by a deafening noise as Inter’s first shot at Champions League glory since their 2010 success was confirmed.
Simone Inzaghi was happy to accept that Tuesday’s second leg represented “one of the most important games in Inter’s history” and the Italian showed faith in the same 11 that arguably should have ended the tie as a contest a week earlier.
He and his players would have expected a different match – including an intense start from their historic rivals – as they returned in front of a feverish 80,000-strong San Siro crowd to play out the conclusion of the first Milan derby in European competition for 20 years.
That was exactly what they faced as seven-time winners Milan pressed for an early goal in an attempt to ignite a memorable comeback, with Diaz and Leao both going agonisingly close.
However, they had to rely on goalkeeper Maignan to keep alive their hopes at the other end of the pitch, with the alert France international also producing a superb stop to deny Nicolo Barella before seeing the offside flag raised.
But any hopes of a late fightback were extinguished by Martinez’s well-taken finish and, for just the second time ever, the Inter supporters were able to enjoy a fourth win over Milan in a single season, as their side comfortably managed the closing stages.
Inter will go into the final against Real Madrid or Manchester City as underdogs, and they will require a near-perfect performance to overcome either.
But Inzaghi’s side will be quietly confident of causing an upset, having not trailed in any knockout-stage match in this season’s Champions League and keeping a competition-leading eight clean sheets.
When is the Champions League final?
The 2023 Champions League final, featuring Inter Milan and either Manchester City or Real Madrid, will take place in Istanbul, Turkey on 10 June at 20:00 BST.