Williamwood High School, in Clarkston, has come top of The Herald's league tables with 45% of its fifth-year pupils achieving five Highers in the summer.
Another East Renfrewshire School – St Ninian's High School in Giffnock – came second in the table with 43% of pupils achieving the benchmark.
East Renfrewshire also topped the league table of councils, with 32% of pupils across the local authority achieving five or more Highers.
The league tables also highlighted the continuing slide of Jordanhill, in Glasgow, the only state-funded, but independently run school in Scotland.
The school has routinely topped The Herald's league tables over the past few years, but slipped from third in 2011 to seventh this year, with 36% of pupils achieving the benchmark.
John Sinclair, the headteacher of Williamwood High, welcomed his school's performance, but said he was not surprised by the success of pupils.
"We have very able pupils and the levels they've achieved this year are no different from the level of achievements over the last four or five years," he said.
"That is matched by some equally talented and hard- working staff who are not complacent about what they do, but who are determined each year to improve on what they've done in the past."
A spokesman for East Renfrewshire Council said the council-wide figures were a testament to the drive from the education department to raise attainment.
"Early intervention, breaking down barriers to learning, and encouraging and promoting achievement in its widest sense, has helped provide the climate and support to continuously improve standards of attainment," he said.
"There is a focus on getting the basics right, maximising the learning time, the use of assessment and monitoring and tracking pupil progress building on prior learning."
Although those schools at the top of The Herald's league tables were rightly celebrating, it is important to put the information published into perspective.
While the table of the 60 top schools highlights those with the highest exam performance, it does not necessarily make them the best schools.
It also raises important questions about those schools where just a few pupils go on to achieve five or more Highers by the end of S5.
Liz Smith, education spokeswoman for the Scottish Conservatives, said there was a worrying trend between the best and poorest-performing schools which "chimes with warnings that many of our secondary children are not achieving a good standard of literacy".
Hugh Henry, education spokesman for Scottish Labour, said the figures highlighted a two-tier schools system. "One for the better-off and one for the poorest, and in too many places the gap is growing," he said.
Larry Flanagan, general secretary of the Educational Institute of Scotland, called for greater funding for schools in deprived areas to provide more support to pupils.
Analysis of the council table underlines just how much deprivation impacts on results.
The lowest-performing local authority areas all have a much higher proportion of pupils on free school meals than the national average of 15.5%, a key indicator of poverty.
Glasgow, the lowest-performing mainland council area, has nearly 30% of its pupils on free school meals compared to just 10% in neighbouring East Renfrewshire.
The tables are particularly illuminating where they identify outperforming local authorities – or those whose performance is less successful than other areas coping with similar deprivation.
One council that stands out is Inverclyde. It covers some of the most deprived communities in Scotland with more than 21% of pupils on free school meals, but still came eighth in our table.
Albert Henderson, Inverclyde's corporate director of education, said: "There is no magic answer, but we have very high expectations for the youngsters and we have invested strongly in education to ensure the best for pupils."
Stephen Curran, Glasgow's executive member for education, defended the city's schools, pointing to steady progress over the last few years.
He also highlighted schools such as Hillhead High, in the west end, which has seen a dramatic improvement in results with 21% of pupils achieving the benchmark despite having nearly 40% on free school meals.
"Glasgow's parents should be assured that the education of their children is in safe hands and I promise we will continue to raise expectations," he said.
A Scottish Government spokesman said: "This year we saw Scotland's pupils achieve the best exam results since records began."