Saturday sees Croatia face the host nation for a place in the semi-finals and Rakitic praised midfield partner Luka Modric ahead of the game.
In the previous 120 minutes, Denis Cheryshev rifled Russian Federation in front with a long-range thunderbolt, his fourth goal of the tournament, in the 31st minute before Andrej Kramaric headed Croatia level six minutes before halftime. Vida makes it 2-1 in the 100th minute.
Goalkeeper Danijel Subasic went into extra time with an apparent right leg injury he picked up in the 89thminute.
Domagoj Vida had scored earlier for Croatia in extra to take the lead after the two played to a 1-1 draw through 90 minutes.
A total of 32 national football teams entered the 2018 FIFA World Cup, but narrowed down to 16 as they proceeded to the knockout phase after the group stage, held between June 14 and 28.More news: As Trump heads for Europe, trade strains start to show
After a pair of the quarterfinal matches played on Friday, team France enjoyed a confident defeat of 2-0 over Uruguay in the city of Nizhny Novgorod, while Belgium went for 2-1 win over the legendary Brazilian team in the city of Kazan.
But the fans also celebrated how far their team - the lowest-ranking side to qualify for this year's World Cup - had come, with crowds dancing and chanting "Russia" in the streets.
They have quickly been embraced as national heroes, with the mayor of Moscow responding by making additional public viewing space available in the city before the match in Sochi's Fisht Stadium.