An opportunistic strike from Robert Snodgrass proved enough for the visitors to claim their first victory of the 2014 World Cup qualification campaign in Zagreb
The hosts suffered a frustrating first half as they were unable to score despite a string of good chances.
That left them vulnerable to the sucker punch, which was provided by Robert Snodgrass' opportunistic strike.
Igor Stimac's side huffed and puffed after the break but failed to break down a resolute Scotland defence.
Gordan Strachan made six changes to the side which lost their last qualifier to Serbia. Leigh Griffiths was the surprise inclusion, making his first competitive appearance for Scotland ahead of Blackburn striker Jordan Rhodes.
Former Tottenham duo Luka Modric and Vedran Corluka both missed the game for the hosts through suspension; otherwise Stimac had a fully fit squad to select from.
The hosts made a quiet start to the game on a warm night in Zagreb, allowing Scotland to see plenty of the ball early on. The visitors, though, were not able to fashion any real chances despite periods of possession.
Darijo Srna was Croatia's main instigator in the first half, bombing up and down the right flank. The Shakhtar Donetsk captain's crosses looked like the hosts's best bet for a goal during a dour first period, but Mario Mandzukic repeatedly struggled to meet his team-mate's deliveries in the box.
They soon paid for their casual start as Scotland stunned the Stadion Maksimir and took an unlikely lead.
Shaun Maloney picked up the ball near the halfway line and ran straight at the heart of the Croatia's defence when Srna's attempt at a tackle inadvertently took the ball into the path of Snodgrass. The Norwich man was alert enough to prod the ball past Stipe Pletikosa with an outstretched leg.
The hosts's best chance of the half came when Grant Hanley played a sloppy ball back to Alan McGregor under pressure from Mandzukic. Following a ricochet, the ball fell to Sammir at the edge of the area but the Brazilian-born midfielder couldn't keep his effort below the bar.
Ivica Olic fired a shot over the bar following a good turn in the box, Ivan Rakatic missed with a header and Srna continued to threaten with his deliveries as Stimac's men began to up the ante.
Strachan's men, though, sat deep and absorbed the pressure well until the break.
It took an hour before the Croatian's genuinely threatened again as Mandzukic came agonisingly close to turning in Rakitic's dangerous low cross from the left wing.
Eduardo and Nikola Kalinic both came on for the hosts as they went all out in search of an equaliser, but a couple of long range strikes from Sammir is all they could muster.
Frustration was etched across Stimac's face as the game entered the final few minutes but despite plenty of probing, his players met the Scotland defence in impenetrable form on the night.