Five-time winner Sevilla came from behind to beat Manchester United on Monday (AEST), and Antonio Conte's side joined them in the final with a rampant victory – Martinez and Lukaku the stars.
Martinez's first Europa League goal of the season got Inter off the mark, and he had his second with 16 minutes left after Danilo D'Ambrosio had doubled the Nerazzurri's lead.
Inter were not done there, though, with Martinez brilliantly teeing up Lukaku, who subsequently helped himself to a second with a terrific turn and finish late on as the Serie A runners up made it into their first European final since 2010.
Martinez's opener came after 19 minutes – Andriy Pyatov slicing a clearance straight to Nicolo Barella, who delivered a pinpoint cross from which Inter's forward headed home.
It should have been 2-0 before the half-hour, but neither Lukaku or Barella were able to tuck in from point-blank range.
Barella would have made up for the miss soon after, had Pyatov not kept out the midfielder's dipping effort.
Martinez nearly caught Pyatov off his line early in the second half, with the goalkeeper just managing to recover, before Lukaku sent a low effort wide.
Junior Moraes should have done better with a header he directed straight at Samir Handanovic just after the hour and Inter swiftly made their fortune count.
Afforded a free run from Marcelo Brozovic's corner, D'Ambrosio leapt highest to plant a firm header beyond Pyatov, who was beaten again when Martinez slotted in his second 10 minutes later.
Martinez then turned provider to cap off a supreme display – Lukaku coolly curling home from inside the area.
Lukaku had his 16th Europa League goal in 10 appearances soon after, adding further gloss to a win that takes Inter to the verge of winning their first trophy since 2011.