Steve Clarke's side took a shock lead through Ryan Christie's first-half goal at the Stadion Maksimir.
But Igor Matanovic equalised before the interval and Kramaric bagged the winner midway through the second half.
Scotland have lost four successive games for the first time since 2019.
They arrived in Zagreb winless in their last eight competitive matches, the longest streak in their history, and that dismal run has now reached nine.
Scotland have mustered just one win in their last 15 matches, a 2-0 victory over minnows Gibraltar in June.
"I thought we were brave with the ball. We tried to play, tried to create chances. On another night we would've got what we deserved," Clarke said.
Having crashed out of Euro 2024 at the group stage, the Scots sit bottom of Nations League Group A1 after defeats against Poland, Portugal and Croatia.
In Clarke's defence, he is dealing with a debilitating injury list that denied him the services of James Forrest, Kieran Tierney, Jack Hendry, Tommy Conway, Aaron Hickey, Nathan Patterson and Lewis Ferguson.
Even so, another loss when Portugal visit Hampden Park on Tuesday would add to the pressure on the Scotland boss.
"We'll go away lick our wounds and prepare to go again on Tuesday," he said.
"A full squad fit and healthy would be a help. There's so much disappointment in the dressing room, but I feel like we're on the right path.
"We haven't regressed. We just have to keep believing, keep pushing away."
Croatia hit back
Scotland started brightly and Christie fired just wide after Andrew Robertson's cross wasn't cleared, while Billy Gilmour tested Croatia keeper Dominik Livakovic with a 25-yard blast.
Craig Gordon, Scotland's 41-year-old stand-in keeper, made a fine save to keep out Kramaric, with Borna Sosa heading just wide from the rebound.
Ben Doak, 18, was the youngest player to start a competitive match for Scotland since Willie Johnston in 1965.
And the Liverpool winger, currently on loan at second tier Middlesbrough, made his landmark occasion even more memorable with the cross that produced Scotland's 33rd-minute opener.
Josip Sutalo made a hash of clearing and Christie gleefully pounced to slot home from an acute angle.
Croatia were behind for just three minutes as Matanovic met Ivan Perisic's clever cutback with a powerful strike that flashed past Gordon.
Matanovic nearly scored again immediately after the interval but this time Gordon was equal to his shot from the edge of the area.
Gordon made another good save to repel a curler from Luka Modric, who deftly nutmegged Scott McTominay before bending his shot narrowly wide in another threatening raid from the evergreen Real Madrid midfielder.
Croatia were well on top and Kramaric completed their comeback in the 70th minute.
Sosa met Perisic's cross with a stinging strike that was parried by Gordon, with Kramaric perfectly placed to head in the rebound.
In a dramatic finale, Che Adams thought he had salvaged a stoppage-time equaliser but VAR disallowed his effort for offside.
