The host country's PM was clearly not amused and chose to look the other way as Croatia's first female President enjoyed every moment of her team dumping Russia out of the tournament.
The Russians, riding a wave of euphoria after unexpectedly knocking out Spain in the previous round, were determined to carry on to a first World Cup semi-final since the break-up of the Soviet Union.
Brazilian-born Mario Fernandes had kept Russia's dream alive when he headed home in the 115th minute to level the scores and force penalties, but he and Fedor Smolov both failed to convert their spot-kicks in Sochi.
Croatia, for whom Andrej Kramaric and Domagoj Vida had earlier found the net, advanced to their first World Cup semi-final since 1998.
They will face England, who beat Sweden 2-0 earlier, at the Luzhniki Stadium Moscow on Wednesday. In contrast for Russia, who had taken the lead through another Denis Cheryshev wonder goal in the first half, there is only heartbreak as they finally go out.