The Croatian state had argued that the separate classes were intended to help Roma catch up with other pupils.
Fifteen former pupils of Roma origin had alleged that the arrangement was a form of racial discrimination and violated their right to education.
Croatia has been told to pay each one 4,500 euros (£4,075) in damages.
In 2008, the European Court of Human Rights in Strasbourg had rejected the former pupils' arguments, but that verdict was overturned by an appeal court on Tuesday.
Eight years have passed since the pupils first argued their case in Croatia - which is currently negotiating accession to the European Union.
All have now left school, and some have small children of their own, the BBC's Nick Thorpe reports from Croatia.
The former pupils attended primary school in the villages of Macinec and Podutren, in northern Croatia, at different times between 1996 and 2000.
The court judgement says the drop-out rate among Roma children in primary school was 84%.
"The court held that no adequate safeguards had been put in place at the relevant time to ensure sufficient care for the applicants' special needs as members of a disadvantaged group," the ruling said.
The court found that Croatia had failed to address the former pupils' alleged deficiency in the Croatian language through any special tuition.
Allocation of the former pupils to Roma-only classes had been done on the basis of a general "psycho-physical" assessment rather than a language test, the judgement said.
The court also said Croatia had violated the plaintiffs' rights to a fair trial because the judicial proceedings had been conducted over an "excessive" period.
BBC News
