The win means Croatia finished second behind England in Group D while Czech, who also qualified, ended in third.
Scotland have now been eliminated at the group stages in all 11 of their appearances at major tournaments (Euros and World Cup).
With both sides knowing a win would grant passage to the last 16, Nikola Vlacic gave Croatia an early lead on 17 minutes to silence the national stadium in Glasgow.
However, a thundering drive in the 42nd minute from Scotland’s Callum McGregor made it 1-1.
But Luka Modric’s sumptuous first-time shot with the outside of his right boot put Croatia 2-1 ahead before Ivan Perisic glanced in a third on 77 minutes from Modric’s corner record Croatia’s first-ever win over the Scots.
The group’s other game saw England pip Czech Republic 1-0 thanks to a Raheem Sterling header.
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