England appeared well-placed to reach their first World Cup final since 1966 when Kieran Trippier put them ahead with a fine early free-kick in Moscow.
But Croatia rallied after the break and Perisic got the goal to peg England back, producing a flying finish after Sime Vrsaljko’s deep cross.
Mario Mandzukic then completed the turnaround in extra time, finishing off England to successfully get beyond the last four for the first time after losing to France in the semi-finals 20 years ago.
When asked where he was during that game in 1998, Perisic told reporters: “I was back in my hometown, rooting for Croatia in my jersey.
“I could only dream of scoring one of the most important goals to send Croatia into a final.”
But he is wary of a France team which has improved steadily throughout the World Cup and looked solid defensively against Belgium’s considerable attacking prowess on Tuesday.
“We saw almost all of France’s games in the group,” Perisic added. “They have played well enough to progress, and upped their game over the past several games.
“They knew that Belgium was strong on the ball. Everybody expected Belgium to progress after beating Brazil, but France can play a defensive game as well.
“Their players play at the top clubs. They have an excellent coach and excellent players.”