St Ninian's High School, in Giffnock, came top of The Herald's school league tables with 53% of its fifth year pupils achieving at least five Highers.
Two other East Renfrewshire schools came second and third.
Williamwood High School, in Clarkston, came a close second with 52.5% of pupils getting five or more Highers and Mearns Castle High School, in Newton Mearns, came third, with 49% attaining the benchmark.
Jordanhill, in Glasgow, the only state-funded but independently-run school in Scotland, came fourth while Tarbert Academy, in Argyll and Bute, came fifth.
John Docherty, headteacher at St Ninian's, described the school's results as "fantastic".
He said: "Our approach is to focus on the needs of every individual pupil and direct our attention and expertise on encouraging each to achieve their potential.
"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."
East Renfrewshire Council also topped the table for overall council performance, with 39% of its pupils getting five or more Highers compared to a Scottish average of 13%.
The council has seen a remarkable seven percentage point increase in its performance compared to last year, stretching the gap between itself and other local authority areas.
In 2012, East Renfrewshire was just four percentage points above its nearest rival East Dunbarton-shire, but this year the gap has stretched to 12 points.
Apart from East Renfrewshire, the rest of the top five councils in our table all either lost ground on last year or maintained the same performance.
Mhairi Shaw, East Renfrew-shire's director of education, said: "These results are a testimony to the phenomenal success of our education service in never resting on its laurels and always striving for improvement.
"Hard work and dedication from our pupils, teachers, education staff and parents have resulted in the successes and we are always looking to invest in our education and better our school portfolio for the future."
Although those schools at the top of The Herald tables are rightly celebrating, it is impor-tant to put the exam information published into context. What is interesting about the list of the top 50 schools in Scotland is the number of them that serve areas of relative affluence compared to the Scottish average.
The simplest way of highlighting this is to use the proportion of pupils at each school in receipt of free school meals.
The table shows that none of the top 50 schools have a higher proportion of pupils on free school meals than the Scottish average of 15.4% and many have significantly lower numbers.
St Ninian's has only 6.2% of pupils on free school meals, Williamwood has 5.1% and Mearns Castle 6.9%. Only St Margaret's Academy, in West Lothian, has a percentage of pupils on free school meals which matches the national average.
The trend continues in the local authority table of performance. Only one council area out of the top 10 in exam performance has a free school meals pupil proportion higher than the national average - South Ayrshire on 16.5%, although Edinburgh comes close. The bottom of the table is an equally good example of the impact of poverty on exam results.
Only one council in the bottom 10 has a free school meals proportion that is lower than the national average and some, like Glasgow, which sits at the foot of the table, has nearly double the national proportion.
The table also shows the councils punching above their weight, such as Edinburgh, South Ayrshire, Renfrewshire and West Lothian.
Despite the impact of poverty, the performance of some councils and schools does raise important questions. Govan High School, in Glasgow, for example, had none of its 60 pupils achieving the lower benchmark of three or more Highers this year.
Larry Flanagan, general secretary of the Educational Institute of Scotland teaching union, said the problem of deprivation was still far from being solved. He said: "Depriv-ation continues to impact adversely on the attainment of too many pupils and this is an area which needs to be addressed as we move forward."
However, Stephen Curran, Glasgow's executive member for education, believes Glasgow's position at the bottom of the league tables does not reflect the significant improvements made over the past few years.
Breaking the figures down further shows Glasgow has gradually increased its proportion of pupils achieving five or more Highers - from 6.8% in 2011 to 8.4% this year.
Mr Curran said: "Not only have we recorded the best ever exam results, our recently published destination figures prove we are also closing the gap with the rest of the country with more of our children going on to education, training or employment."
Dr Alasdair Allan, Minister for Learning, said figures released by the Organisation for Economic Co-operation and Development earlier this month also showed Scotland was "beginning to address the attainment gap".