The 30-share index rose by 301.61 points, or 1.48 per cent, to 20,701.03 points with all sectoral indices, led by banks and realty, gaining up to 2.60 per cent. The index had gained 205.02 points on Thursday.
The stock market remained closed on Friday on account of "Muharram".
The National Stock Exchange Nifty moved up by 83.70 points, or 1.38 per cent, to 6,139.85.
Brokers said sustained buying by funds and retail investors tracking a firming trend on other Asian bourses, as US markets surged to new record highs on Friday after Federal Reserve chief nominee Janet Yellen bolstered expectations of the Fed keeping the flow of easy money, mainly buoyed the trading sentiment here.
The US Dow Jones Industrial Average gained 0.54 per cent to close at fresh record high on Friday.