St Andrews University was rated the best in Scotland and the fourth-best in the UK, after Cambridge, Oxford and the London School of Economics, in the latest edition of the Complete University Guide.
The 600-year-old Fife institution was the only seat of learning in Scotland to make it into the UK top 10 in the 2015 guide, with Edinburgh university - which has traditionally battled St Andrews for the top spot in Scotland - falling out of the top 20 for the first time in six years.
Both universities have the highest levels of intake from private schools - about 40 per cent of St Andrews students and 30 per cent of Edinburgh students were educated in the independent sector, compared to around 12 per cent of students admitted to Glasgow university.
St Andrews, also attracts a high proportion of overseas students, particularly from North America.
The league table rates universities on the basis of factors including graduate prospects, entry requirements, research and student satisfaction. It also takes into account the staff-to-student ratio, proportion of good honours degrees achieved and spending on facilities.
It is the second year in a row St Andrews has been ranked the best in Scotland and fourth in the UK.
Edinburgh University remains in second place in Scotland but has fallen three places to 21st for the UK as a whole. Glasgow University has dropped further, from 23rd to 30th, its lowest ranking since 2008.
In separate listings covering 67 subjects, Edinburgh was rated best for nursing studies with Glasgow top for veterinary medicine. Meanwhile, Strathclyde University is rated best in the UK for medical technology, with Glasgow Caledonian university best for complementary medicine.
Dr Bernard Kingston, principal author of TheCompleteUniversityGuide.co.uk, said: "The league tables, taken with the rankings for specific subjects, offer would-be students an accurate and independent guide to the UK university system.
"They should not be used in isolation but alongside all the other advice and information in the guide. Its tables are recognised for their stability and consistency, and this year once again demonstrates this.
"Many of the changes this year are attributable to changes in definitions and weighting.
"There was an official and fundamental review of the staff record data between the two years, while the old distinction between graduate and non-graduate employment has been replaced by one between professional and non-professional employment."