For the second year in a row, the University of Oxford was tops.
NUS and NTU have been rising up the rankings since 2012. That year, NUS jumped 11 places to the 29th placing, while NTU improved by 83 places to be ranked 86th.
1. University of Oxford
2. University of Cambridge
3. California Institute of Technology
3. Stanford University
5. Massachusetts Institute of Technology
6. Harvard University
7. Princeton University
8. Imperial College London
9. University of Chicago
10. ETH Zurich
10. University of Pennsylvania
22. National University of Singapore
52. Nanyang Technological University
• For the full list, go to www.timeshighereducation.com/world-university-rankings/2018/world-ranking.
Mr Phil Baty, editorial director of the Times ranking, said NUS and NTU have surpassed leading varsities in the United States this year.
NUS has overtaken Carnegie Mellon University in Pennsylvania, placed at 23rd; NTU has beaten the University of California, Davis.
"While NUS has risen to become Asia's leading university in recent years, the 26-year-old NTU has leapt a staggering 122 places since 2010-11, thanks to continued high levels of investment, outstanding research and a highly international outlook," added Mr Baty.
Singapore's good showing is part of a wider Asia trend, he said. In a first under the ranking's current methodology in use since 2011, three Asian universities are in the top 30 - NUS and China's Peking and Tsinghua universities, ranked 27th and 30th respectively.
NUS was placed among the world's top 20 universities in research, teaching and international outlook. NUS president Tan Chorh Chuan said he is delighted at NUS' good showing in the rankings and said it will focus on preparing graduates for the future economy and strengthening lifelong education.
NTU, which overtook NUS for the first time in the Quacquarelli Symonds World University Rankings released in June, said these rankings showed it is "continuing its upward march globally". NTU had moved up to 11th place, while NUS fell from 12th to 15th.
NTU president Bertil Andersson said: "The two league tables demonstrate the high regard that academics, researchers and industry leaders worldwide have for NTU, despite the increasingly competitive global higher education sector."