Zlatko Dalic's men defeated tournament hosts Russia 4-3 on penalties after a topsy-turvy 2-2 stalemate in Sochi on Saturday.
Vida, 29, headed Croatia in front in extra time, only for his effort to be cancelled out by Russia's Mario Fernandes in the dying embers of a thrilling encounter.
And the Besiktas man stepped up once again for his country by converting a spot-kick in Croatia's second shootout win of the competition.
Vida has since revealed that he had actually volunteered to take a penalty, with manager Dalic having only four takers in mind initially, and the defender received some tips from Rakitic before scoring.
"I went to Rakitic for advice and he told me just to pick a side and not change it,” Vida told Croatian media after the match.
“Then I went to our assistant coach Drazen Ladic and he told me to think of something nice. So I took both tips, picked a side where to shoot and thought about my wife and son.”
Vida even considered attempting a Panenka penalty, only to revert to a safe effort after seeing Russia striker Fedor Smolov fail in his attempt earlier in the shootout.
He added: "Yes, I was crazy enough that I considered a Panenka!
“But the first Russian guy (Smolov) took it and missed so I gave up.”
Croatia will now lock horns with England for a place in the World Cup final in Moscow on Wednesday.