The 30-share index, which had gained 358.73 points in the previous session, shot up by 100.25 points, or 0.48 per cent, to trade above 21,000 level at 21,029.26.
The wide-based National Stock Exchange index Nifty rose by 30.00, or 0.48 per cent, to 6,250.90.
Brokers said sentiments buoyed on hopes of liquidity enhancement after the RBI cut the marginal standing facility rate to 8.75 per cent and a firming trend in the Asian region fuelled by expectations the US Federal Reserve will maintain its aggressive stimulus.
In the Asian region, Japan's Nikkei gained 1.22 per cent, while Hong Kong's Hang Seng was up by 0.70 per cent in early trade today.
The US Dow Jones Industrial Average rose 0.72 per cent to close at fresh all-time high in yesterday's trade.