The party said pupils from well-off backgrounds were seven times more likely to get three Higher A grades than those from poorer homes.
Tory leader Ruth Davidson revealed the statistics as she challenged Nicola Sturgeon on the issue at Holyrood.
Ms Sturgeon said there had been some progress in closing the gap.
She said 40% of pupils from the 20% most deprived areas getting at least one higher, up from 23% in 2007.
And the first minister said 300 primary schools across the country were already benefiting from support through a Â£100m attainment fund.
But she acknowledged: "I am not standing here, I never have stood here and said that there's not more work to do.
"But we are seeing in many respects evidence of the attainment gap narrowing."
The Conservatives said the figures released to them under freedom of information legislation showed that, of S5 pupils who sat Higher exams last year, 21.13% of the most privileged achieved three As, up from 20.31% in 2013.
But in the poorest fifth, just 2.99% got three As, compared to 2.90% the year before.
The Conservatives said that meant the attainment gap increased by almost 1% between 2013 and 2014, despite SNP pledges to close it.
The statistics showed that in four council areas - Argyll and Bute, Dumfries and Galloway, East Lothian and Midlothian - not a single pupil from the most-deprived areas attained three As in their Highers.
Ms Davidson also cited a report by the Commission for School Reform which earlier this week questioned the Scottish government's ability to close the gap.
The commission, chaired by educationalist Keir Bloomer, said that while few would disagree with ministers' desire to tackle the issue, their policy priorities were "exceptionally ambitious" and the timescale "may well be unrealistic".
Ms Davidson said: "We knew that the SNP government was not closing the attainment gap but now from these figures we know that that gap between the richest and poorest students is actually getting wider.
"The first minister has said that she wants to be judged on her record. In education, her record is one of failure and the experts say that her plans won't fix it.
"How bad do things have to get before we see the action we need?"
Liberal Democrat leader Willie Rennie criticised the government's plans for standardised testing.
He said: "The first minister told me she was against league tables but she has told journalists that she is not going to stop them putting primary schools into league tables.
"If she doesn't want them, why is she going ahead and taking all the steps to make them happen?"
Ms Sturgeon responded: "I stand by what I said. I have no interest in crude league tables that offer no meaning to parents, nor do I have any interest in a system that would encourage teaching to the test.
"But I do think it is incumbent on me as first minister to make sure that children's progress is being assessed in a way that better informs the judgements teachers make about their performance."
The attainment gap between pupils from the wealthiest and least well off backgrounds has widened, according to the Scottish Conservatives.