Just when England appeared set for victory after Anthony Gordon's second-half goal, Argentina mounted a relentless late siege and got their reward as Fernandez levelled before Martinez completed the turnaround in the 92nd minute with Messi providing the pass for the equaliser and the cross for the winner.
For England, dreams of a first World Cup final since 1966, when they enjoyed their only triumph at the global tournament, were dashed in the closing stages, while Argentina celebrated a comeback that kept alive their quest for another world title.
With England inexplicably parked in their own end, an Argentina equaliser felt inevitable and, after waves of late pressure, Fernandez finally broke through in the 85th minute when Messi found him in space on the edge of the box to fire home from 20 metres past Jordan Pickford into the corner.
Martinez, an 81st-minute substitute, struck the winner early in added time when Alexis Mac Allister drove a shot off the post that Messi recovered. The 39-year-old talisman drove down the right to send in a brilliant ball for Martinez to head home.
Argentina will face Spain in the World Cup final on Sunday at MetLife Stadium in New Jersey.
