After a slow start with Croatia controlling the ball, Scotland took the lead in the 32nd minute when defender Josip Sutalo's failed clearance landed perfectly for Ryan Christie of Bournemouth. Christie quickly turned and managed to slot in a shot from a difficult angle, giving Scotland the opening goal.
Sparked into action, Croatia hit back four minutes later as Ivan Perisic’s pin-point cutback was driven into the bottom corner through a sea of Scotland defenders by Igor Matanovic for his first international goal.
Croatia continued to press forward after the break and Hoffenheim forward Kramaric scored the crucial goal when he headed home a rebound from close range after Scotland keeper Craig Gordon kept out a crisp volley from Borna Sosa.
Scotland thought they had nabbed a late equaliser in the 95th minute when Che Adams was quickest to react to a loose ball in Croatia’s penalty area, but the Torino forward was adjudged to be offside after a VAR review.
Croatia are second in League A Group 1 with six points, level with leaders Portugal, who face Poland later on Saturday. Scotland, who have suffered three defeats, remain bottom with no points.