But they now need to work out how to score their first goal because a draw is no good for them in their final match of Group D.
Croatia reached the final of the 2018 World Cup, so a group stage exit at the Euros would be bitterly disappointing.
Here’s everything you need to know ahead of the game.
When is the match?
The game kicks off at 8pm on Tuesday 22 June at Hampden Park.
Where can I watch it?
The match will be shown live on ITV2 and S4C, and can be streamed online via the ITV Hub.
What is the team news?
Clarke is without Billy Gilmour and could opt for either Ryan Christie or David Turnbull to replace him.
Croatia are not said to have any injury issues heading into their final Group D encounter.
Croatia XI: Livakovic, Perisic, Lovren, Kovacic, Modric, Brozovic, Vlasic, Petkovic, Vida, Juranovic, Gvardiol
Scotland XI: Marshall; McTominay, Hanley, Tierney; O’Donnell, Armstrong, McGregor, Robertson; McGinn; Dykes, Adams
Croatia - 23/20
Draw - 11/4
Scotland - 2/1
Scotland can make history by reaching the second round of a major tournament for the first time. But while Croatia are not the team they were three years ago, they still have more pedigree than the Scots at the European Championships and also need a win to qualify. 1-1.