Kolinda, the first female president in her country, was earlier seen shaking hands and congratulating Medvedev when Russian Federation took the lead but she couldn't hide her excitement when her team entered the semi-final for the first time after 1998.
Here, Press Association Sport takes a look back at when Croatia last reached the final four at France 98.
Eight of England's 11 goals so far have come via free kicks, corners or penalties, which is four more than any other team and the most since Portugal also scored eight set-piece goals at the World Cup in 1966.
Croatia want to party like it's 1998 at the expense of hosts Russian Federation in Sochi on Saturday when the two sides meet in their World Cup quarter-final.
Luka Modric won the man of the match award for the third time in five games at this World Cup, with a superb array of passing from a deep role in midfield. Vida told Croatian media after the match said via Goal.
After beginning his coaching career at the age of 28 with FC Vevey in Switzerland, Miroslav Blazevic managed several clubs, most notably Dinamo Zagreb, before taking the Croatia helm in 1994.
Croatia was ousted in the group stage in 2002 and 2006, didn't qualify for 2010 in South Africa and was again dumped in the group stage in 2014 - albeit from a very hard group.
At the blast of the final whistle, Croatia president Kolinda Grabar-Kitarovic rushed into the dressing room to celebrate with the players.
"It makes us extremely proud and happy that after 20 years we've reached the semi-final of a World Cup", the former Tottenham midfielder said.
The two sides couldn't be split after 120 minutes as the match ended in a 2-2 draw and it was Croatia who held its nerve best.
Robert Prosinecki, a member of the 1998 squad, said: "I would so much like that they be better than us".
More than 24,000 fans attended a meeting with the national football team in Moscow to thank the players for their historic World Cup performance, which saw them progress to the quarter-finals for the first time in their history.
Every match at this World Cup is like that.
Croatia sealed their spot at the ongoing FIFA World Cup after defeating hosts Russian Federation 4-3 on penalties.
I am playing in the quarter-finals. "We need to move forward and I think we believed in our strength and in ourselves".
The managers at two bars in Moscow that have been showing World Cup games said their venues had been packed to the rafters whenever Russian Federation was playing, but that they did not expect the high demand to continue.
He's ready to face the music now and says "it's nice to hear people enjoying it again".