The blue-chip NSE Nifty 50 index ended up 0.71% at 11,521.80, while the benchmark S&P BSE Sensex closed 0.74% higher at 39,044.35.
London's benchmark FTSE 100 index of major blue-chip companies shed 2.1 per cent to 5,882.30 points, compared with Friday's closing level.
Most Asian markets fell Monday following another disappointing performance on Wall Street with investors growing concerned about an uptick in coronavirus infections in Europe and the United States, as well as the lack of movement in Washington on a new stimulus.
The benchmark Nikkei 225 index gained 0.65 per cent, or 152.81 points, at 23,559.30, while the broader Topix index was up 0.88 per cent, or 14.46 points, at 1,651.10.
The pan-European STOXX 600 index fell 0.8%, recovering slightly after hitting its lowest level since June 26, while bourses in Frankfurt, London and Paris were down between 0.3% and 0.6%.
The MSCI index is also set for its biggest weekly drop since March, down more than 4% so far this week. Chinese blue-chips dropped 1.6%, Hong Kong's Hang Seng fell 1.7%, Seoul's KOSPI sank 2.59% and Australian shares fell 0.81%.
Japan's Nikkei declined 1.11%.
At 8:36 a.m. ET, Dow e-minis were down 163 points, or 0.61%, S&P 500 e-minis were down 24.5 points, or 0.76%, and Nasdaq 100 e-minis were down 139 points, or 1.28%.
The pan-European STOXX 600 index slipped 0.1%, failing to match Asian and Wall Street gains , France's CAC 40 fell 0.7% after the country set a new record of daily COVID-19 infections.
The pan-European STOXX 600 index rose 1.7% after last week's 3.6% drop, with the banks index jumping 4.1%.