The Tartan Army opened the scoring in the 33rd minute courtesy of Ryan Christie, who admittedly benefitted greatly from Luka Sucic's sliced clearance in the box, but Croatia equalised just three minutes later thanks to Igor Matanovic's sweeping finish into the bottom-right corner.
Andrej Kramaric scored his 30th goal for Croatia in the 70th minute after he pounced on Craig Gordon's save with a header from close range.
In the fifth minute of second-half stoppage time, it appeared that Scotland had equalised thanks to Che Adams deflecting the ball off of Duje Caleta-Car, but VAR ruled out the goal to and condemned the visitors to their third defeat in as many Nations League games.
Croatia manager Zlatko Dalic will be pleased that his side have moved three points clear of third-placed Poland, who appear to be Vatreni's main challengers to securing qualification for the quarter-finals via a placement in their group's top two.
As for Scotland, they are yet to pick up any points and Steve Clark's side seem favourites for relegation to League B given they are six points from automatic safety.
Christie's opening goal came about thanks to brilliant work from both Billy Gilmour and Ben Doak, with the former winning the ball back in his own half and the latter driving towards the right of the box before chipping a ball into the penalty area which Sucic failed to deal with.
Matanovic finished well to level the scoreline after Ivan Perisic cut the ball back to him in the box, but credit should also go to Josko Gvardiol for starting the move from just inside Scotland's half.
Perisic was also involved in his side's second goal, crossing towards Borna Sosa, whose shot was parried towards an unmarked Kramaric.
In the closing stages of the game, Kenny McLean flicked the ball into the Croatian penalty area and Che Adams deflected the ball off of Caleta-Car and into the back of the net, but Scotsman was offside when McLean played the ball and VAR chalked off the goal.
CROATIA VS. SCOTLAND HIGHLIGHTS
Ryan Christie goal vs. Croatia (33rd min, Croatia 0-1 Scotland)
Blly Gilmour does brilliantly to win the back possession from inside his own half before Ben Doak carries the ball towards the right of the box and his chipped ball into the danger zone is sliced by Luka Sucic, whose skewed clearance allows Ryan Christie to force the ball over the line despite the best efforts of Duje Caleta-Car.
A horrible error from Sucic!
36th min: Croatia 1-1 Scotland (Igor Matanovic)
Josko Gvardiol picks up the ball from just inside Scotland's half and immaculately switches play from left to right towards Ivan Perisic just inside the penalty, and the PSV Eindhoven player cuts the ball back to Igor Matanovic, who sweeps the ball home from a central area.
What a pass from Gvardiol!
70th min: Croatia 2-1 Scotland (Andrej Kramaric)
Ivan Perisic crosses from the right to the far post towards Borna Sosa, but while Craig Gordon manages to save the shot which was struck into the ground, he can only parry the ball out to Andrej Kramaric, who rises to meet the ball and heads home from close range in the penalty area.
Croatia take the lead with just 20 minutes to go!
95th min: Croatia 2-1 Scotland (Offside goal)
Scotland thought they had equalised with the last kick of the game when Che Adams deflected the ball off of Duje Caleta-Car into the back of the net after the Scotsman reacted quickest to Kenny McLean's flick into the box, but Adams was adjudged to have been offside!
Heartbreak for Scotland!
MAN OF THE MATCH - IVAN PERISIC
Ivan Perisic put in another relentless performance, and managed to get the assist for Matanovic's leveller with a brilliant cutback from the right of the box.
The Croatian was also heavily involved in his side's second goal when he put in a cross towards the back post for Borna Sosa, whose shot was parried into the path of goalscorer Kramaric.
Perisic also created four chances in the match, the most of any player on the pitch, while also winning 100% of his tackles.
CROATIA VS. SCOTLAND MATCH STATS
Possession: Croatia 51%-49% Scotland
Shots: Croatia 17-9 Scotland
Shots on target: Croatia 6-2 Scotland
Corners: Croatia 3-2 Scotland
Fouls: Croatia 14-7 Scotland
BEST STATS
WHAT NEXT?
Croatia will travel to face Poland on October 15 in their final match of the October international break, before facing Scotland once again on November 15.
Meanwhile, Scotland will host Portugal on Tuesday before taking on Croatia and Poland in their final two Nations League group matches in the November international break.