Scottish Government statistics on attainment show a significant gap between those pupils from the most deprived areas and those from the most affluent.
The Conservatives have highlighted figures covering the number of pupils getting three or more Higher As in one sitting, broken down by areas of deprivation, for the years 2012 and 2013.
Across Scotland, around 20% of pupils in the wealthiest communities gained three or more As, while this figure dropped to 2.6% among pupils in the poorest communities.
Edinburgh had the biggest performance gap in 2013, with only 1.1% of children in the poorest areas gaining three As - equating to six pupils. This compares with 22.9% of the capital's wealthiest pupils - equating to 290 children.
An attainment gap is also apparent in many of Scotland's other local authorities, including Dundee, where just 1.8% of pupils in the poorest areas achieved three or more As at Higher grade in 2013, compared with 18.2% in the most affluent group.
In West Lothian, only 3.8% in the most deprived areas achieved three As compared with 29.1% in the wealthiest.
The Tories said the gap suggests education inequalities are "deeply entrenched" throughout Scotland, and called for a "radical overhaul" of the education system. The party wants headteachers to be given more powers to improve their schools, and greater choice for parents in selecting the type of school for their child to attend.
Tory leader Ruth Davidson said: "I do not believe or accept that poorer students are less able - they are simply being failed by a rigid, top-down education system that slams the door on ambition and opportunity for so many."
She said it was time headteachers were given real autonomy to improve their schools.
A Scottish Government spokesman said it was committed to education being based on "the ability to learn, not the ability to pay". It is working to increase access to higher education.
He said: "The most recent figures, published by Skills Development Scotland, confirmed 91.4% of school leavers are now in positive destinations such as employment, college or Higher Education, combined with the achievement of Scotland's best ever exam pass rates last year.
"We are confident that the continuing roll-out of Curriculum for Excellence, the new approach to learning and teaching in Scottish schools, will lead to greater achievement for all pupils in the years ahead."