The recovery in the key indices, analysts believe, came on the back of upbeat global markets.
The BSE Sensex gained as much as 1,112.64 points, or 1.43 per cent to hit an intraday high of 78,387.63 levels. On the other hand, Nifty50 has risen 1.39 per cent, or 326.85 points to an intraday high of 23,780.65.
Most of the sectors gained too. Nifty Media was the top sectoral gainer, surging 3.70 per cent to an intraday high of 1,969.30 levels. Similarly, Nifty IT, Auto, PSU Bank, Realty, Consumer Durables, Oil & Gas rose in the range of 1.83 per cent-2.23 per cent.
The Asia-Pacific markets were mostly trading higher on Tuesday, mirroring gains on Wall Street. Australia's ASX 200 was up 0.89 per cent, while Japan's Nikkei 225 gained 0.49 per cent, and the Topix added 0.61 per cent. South Korea's Kospi edged up 0.07 per cent.
Hong Kong's Hang Seng Index fell marginally (0.04 per cent), and mainland China's CSI 300 dipped a little over 1 per cent.
Overnight in the US, the Nasdaq Composite recovered from a challenging week, closing 0.6 per cent higher, supported by gains in Tesla's stock. The S&P 500 increased 0.39 per cent. Meanwhile, the Dow Jones Industrial Average slipped 0.13 per cent.