The Nations League represents one of the last chances for Croatia's elder statesmen, including Real Madrid midfielder Luka Modric, to taste international triumph.
Croatia then went ahead through Mario Pasalic in the 73rd minute before Noa Lang side-footed the ball into the roof of the net to equalise six minutes into stoppage time.
Bruno Petkovic curled home a stunning shot from the edge of the penalty area 8 minutes into extra time while Luka Modric made sure of Croatia’s triumph with a late penalty.