The hosts took the lead thanks to a superb strike from Denis Cheryshev but Croatia hit back before the break when Mario Mandzukic's cross was headed home by Andrej Kramaic.
The Croatian players were quick to take back the initiative in the game and by the middle of the first half they registered the ball possession at nearly 70% against Russia's slim 30%.
The Croats won all three games to top Group D ahead of second-placed Argentina and then edged Denmark in a penalty shootout after a 1-1 draw.
Croatia hadn't advanced this far at the World Cup since the 1998 World Cup, which was its first appearance.
Bourdain leaves bulk of $1.2M estate to 11-year-old daughter
According to the will, however, if Ariane had passed before Bourdain, his finances would have gone to her nanny, Myra Quizon . Anthony was dating Asia Argento at the time of this death, but the will was written in 2016 while he was still married.
Fast forward just over 28 years and on Wednesday evening in Moscow they will play one again. The English team defeated Sweden 2-0.
Eight more teams left the list of contestants for the 2018 World Cup Trophy in the round of Last 16, which was played between June 30 and July 3. Igor Akinfeev later blocked an attempt from Mateo Kovacic.
Domagoj Vida made it 2-1 for Croatia 10 minutes into the second stanza with a fine header that sailed into the bottom corner.
Rakitic then scored his second penalty shoot-out victor in two games.
Earlier, NAIJ.com had reported how England's Three Lions defeated Sweden 2-0 margin courtesy of two headed goals from Harry Maguire's 30th minute and Dele Alli's 59th minute during Saturday's quarterfinal fixture to book passage into the semifinals of the ongoing FIFA World Cup in Russian Federation.