The 30-share index was trading 322.71 points, or 0.91 %, higher at 35,972.65.
The index had broken its three-day falling streak in the previous session Monday by ending 179.79 points, or 0.51 %, higher at 35,649.94.
The broader Nifty too jumped 88.65 points, or 0.83 %, to 10,818.50 .
The gains on Dalal Street were led by IT, metal, auto and financial stocks.
Top gainers include TCS, Reliance, Infosys, HDFC Bank, ITC, ICICI Bank, IndusInd Bank, Axis Bank, HUL and SBI, rising up to 2 %.
On the other hand, Bharti Airtel, PowerGrid, NTPC, Asian Paints and Hero MotoCorp were the top losers, falling up to 1 %.
Global investor sentiment was boosted after White House economic advisor Kevin Hassett, in a television interview, assured that US President Donald Trump had no intention of firing the chairman of the Federal Reserve Jerome Powell.
Hassett also downplayed jitters over the economic outlook, following plummeting stock market prices.
Dow Jones Industrial Average index had plunged 653.17 points, or 2.91 %, to 21,792.20 in its previous session Monday on reports that US President Donald Trump was weighing options to fire Federal Reserve Chairman .
The rupee, meanwhile, weakened against the US dollar, and was trading at 70.27 a dollar, down 0.27 % from its previous close.
Brent crude, the international benchmark, was down 1.18 % at USD 54.64 per barrel.
On a net basis, foreign portfolio investors (FPIs) bought shares worth Rs 80.28 crore Wednesday, while domestic institutional investors (DIIs) were net sellers to the tune of Rs 137.63 crore, provisional data available with BSE showed.
Elsewhere in Asia, Japan's Nikkei rallied 3.84 %, Hong Kong's Hang Seng was up 0.60 %, Kospi gained 0.16 % and Shanghai Composite Index rose 0.56 % in early trade.