The top Scottish institution is Edinburgh, which came 17th overall and fifth in the UK after climbing four places from last year.
The second ranked institution was Glasgow University, which came 51st after a rise of three places.
St Andrews took 83rd place after climbing 10 places in the rankings.
The survey, run by QS, an international careers and education network, placed US research giant the Massachusetts Institute of Technology at the top of the table for the second successive year, while Harvard moved into second place ahead of Cambridge University.
Education Secretary Michael Russell paid tribute to the success of the Scottish institutions.
"The news reflects the exceptional commitment of staff and students at our universities. We have known for some time that higher education in Scotland is world-renowned and the rankings are further evidence that we punch above our weight in research and education," he said.
"Seeing Edinburgh very much up there with MIT, Cambridge and Harvard is great news for the institution and will further enhance its global reputation.
"I am also very pleased to see Glasgow University's success in achieving its highest ever world ranking and St Andrews very impressively building on their placing last year."
Professor Sir Timothy O'Shea, principal of Edinburgh University, highlighted the recent success of the institution in attracting research funding.
Figures just released show that the university was awarded £300 million in competitive research grants in 2012/13 - up from £250m in 2011/12.
"The news about our research funding figures, and our continued rise in the various world league tables, is very welcome and reflects the quality, hard work and dedication of our staff and students, as well as the highly strategic support we receive from the Scottish Government," he said.
"With such support, the university can go on producing world-leading research which has the potential to change people's lives for the better."
Glasgow University said the improvement followed extra funding in May this year which saw £2.5m from the Scottish Funding Council - which the university matched - go towards world leading research.
Professor Anton Muscatelli, principal of Glasgow University, said: "I am delighted that our progress in these rankings over recent years has continued.
"The QS World Rankings are significant as they confirm the reputation of Glasgow as a world leading research intensive university. In the context of recent Scottish Government funding announcements this is a very pleasing result."
A spokeswoman for Universities Scotland said Scotland regularly punched above its weight in the higher education sector.
"These rankings confirm Scotland's higher education sector is truly excellent in global terms," she said.