The broader Nifty too was trading above the key 10,200- level, up by 81.65 points or 0.80 percent at 10,248.35. The Sensex and the Nifty had fallen in six of the previous seven sessions.
The gauge had rallied 352.03 points Thursday.
All the BSE sectoral indices except Energy were trading higher led by metal, consumer durables, auto, banks and FMCG.
On Wednesday, the key indices were dragged lower by interest-rate sensitive stocks like banking, metals and capital goods.
Brokers said unabated buying by retail and domestic institutional investors and a firm trend in other Asian markets influenced sentiment in Mumbai.
Major gainers in the 30-share index were Bharti Airtel (6.08%), Asian Paints (3.29%), Maruti Suzuki India (3.26%), Tata Steel (2.97%), and Bajaj Auto (2.78%). DIIs had bought shares worth Rs 995.11 crore, while foreign funds sold shares to the tune of Rs 1,217.92 crore yesterday, the provisional exchange data showed. Sensex climbed 242 points or 0.74% to 33,191.75 while the wider Nifty was up by over 76 points or 0.76% to 10,243.60.
In the global markets, Asian shares hovered near two-month lows on Thursday as softer oil and copper prices and uncertainty over United States policy kept many investors on the sidelines, even as some high-tech bellwethers bounced back after a searing sell-off. China's Shanghai Composite Index was quoting in green, up by 0.15 per cent.
Japan's Nikkei was up 1.22 percent while Hong Kong's Hang Seng rose 0.57 percent in early trade today.