The Inter Milan winger poked home a cross from Sime Vrsaljko to haul Croatia level midway through the second half having fallen behind to an early Kieran Trippier free-kick.
Mario Mandzukic completed the turnaround around with the winner on 109 minutes to send his country through to Sunday’s final against France.
“It was a very difficult game. We all know what was at stake and how important a semi-final is for a small country like Croatia,” said Perisic.
“We started slowly, but we showed our character just as in the previous two knockout games when we were a goal down. We didn’t used to be that resilient.”
With a population of just over four million, Croatia are the smallest nation to reach the final match of a World Cup since Uruguay lifted the title in 1950.
“I would like to thank everyone who came to support us in Moscow and everyone back home in Croatia who are sending their incredible support to us.”
The 29-year-old Perisic recalled watching Croatia’s last semi-final appearance in 1998, a game won 2-1 by eventual champions France.
“I was back in my hometown. I rooted for Croatia wearing the Croatian jersey,” said Perisic, who came through the youth teams in France with Sochaux.
“I could only dream to play for my country and to score one of the most important goals.”