With the game tied at 2-2, Duran came off the bench and struck a superb effort from 25 yards with the laces of his left boot to find the top corner and complete Villa's comeback.
Martinez couldn't hide his shock as he put his hands on his head with his mouth wide open after the striker's goal.
Jamie Carragher, who was on commentary for Sky, said: 'You don't see goals like that anymore', before adding simply 'boom' when he saw the replay of the spectacular strike.
It was Duran's third goal from four league games this season having also scored against West Ham on the opening day and Leicester before the international break.
Aston Villa goalkeeper Emiliano Martinez was left in disbelief after Jhon Duran's stunning goal
The stunning goal also continued Villa's bright start to the season, with Unai Emery's men winning three out of four matches so far.
The Midlands side had fallen behind against the run of play when Amadou Onana was pickpocketed before Dwight's McNeil's strike inside 16 minutes.
Dominic Calvert-Lewin doubled Everton's lead 11 minutes later with a header from McNeil, who turned provider.
Ollie Watkins halved the deficit with a close-range header after 36 minutes having leaped over Toffees defender Michael Keane.
The England international then swept home the equaliser just before the hour mark, with Duran then scoring the winner after 76 minutes.