The benchmark Sensex rebounded about 425 points to end well above the 38,000-mark on Tuesday, breaking its two-day falling streak on gains in heavyweights RIL, SBI and ICICI Bank amid persistent foreign fund inflows and positive global leads.
The broader NSE Nifty too inched closer to the key 11,500 mark.
A stronger rupee, which climbed 19 paise to 68.77 against the US dollar (intra-day), also supported the rally, brokers said.
The 30-share Sensex stayed in the green for the better part of the session and hit the day's high of 38,297.70 as buying pace gathered momentum towards the fag-end.
It finally ended at 38,233.41, up 424.50 points, or 1.12 per cent.
The gauge had lost over 575 points in the previous two sessions, tracking a sell-off across global markets.
The broader NSE Nifty climbed 129 points, or 1.14 per cent, to close at 11,483.25 Intra-day, it shuttled between 11,495.90 and 11,352.45.
Oil-to-telecom conglomerate Reliance Industries emerged as a prominent gainer in the Sensex pack, spurting over 3 per cent.
Foreign institutional investors remained net buyers, pumping in Rs 150.40 crore, while domestic institutional investors (DIIs) sold shares worth Rs 12.52 crore Monday, provisional data showed.
Globally, Asian and European stocks bounced back, reversing part of their recent losses, as US treasury yields edged higher, easing concerns about a recession in the world's largest economy.
"After a subdued opening, market bounced back sharply and covered yesterday's losses due to positive global peers. Global growth outlook still remains a concern while rise in US 10-yr bond yield after two days of fall gave some respite to investor sentiment.
"The rebound was broad based except IT index due to strengthening rupee. Gradual fall in FII inflows added some caution among investors which may end up with some consolidation in the near term, after a sharp rally in the short term," said Vinod Nair, Head of Research, Geojit Financial Services.
State-run NTPC topped the gainers' chart in the Sensex pack, rallying 3.28 per cent, followed by SBI at 3.23 per cent.
Other winners were Vedanta 3.18 per cent, ICICI Bank 2.75 per cent, Bajaj Finance 2.72 per cent, Yes Bank 2.71 per cent, Kotak Bank 2.60 per cent, Asian Paints 2.02 per cent, IndusInd Bank 1.84 per cent, Axis Bank 1.79 per cent, HCL Tech 1.73 per cent and HDFC Bank 1.21 per cent.
Sun Pharma, Tata Motors, Maruti Suzuki, M&M, Tata Steel, HUL, Hero MotoCorp, PowerGrid, ONGC and Bharti Airtel too ended with gains of up to 1.11 per cent.
However, Infosys lost 1.23 per cent, Bajaj Auto 0.85 per cent, ITC Ltd 0.68 per cent, L&T 0.37 per cent, TCS 0.26 per cent, Coal India 0.08 per cent and HDFC Ltd shed 0.01 per cent.
Shares of Jet Airways soared for the second day on Tuesday, zooming nearly 7 per cent following the exit of founder and Chairman Naresh Goyal and his wife Anita from the board of the ailing airline.
Coming to sectoral indices, bankex gained 2.19 per cent, power 1.70 per cent, PSU 1.31 per cent, metal 1.11 per cent, consumer durables 1.08 per cent, infrastructure 0.99 per cent, oil and gas 0.97 per cent, realty 0.73 per cent, healthcare 0.61 per cent, FMCG 0.13 per cent and capital goods 0.15 per cent.
IT and teck indices, however, shed up to 0.58 per cent.
Broader markets too were in a better shape in tandem with the overall trend, with the BSE mid-cap and small-cap indices gaining 1.09 per cent and 0.66 per cent.
Elsewhere in Asia, Japan's Nikkei surged 2.15 per cent, while Hong Kong's Hang Seng inched up 0.15 per cent, Singapore's Straits Times rose 0.55 per cent, Taiwan index gained 0.76 per cent and Korea's KOSPI advanced 0.18 per cent. However, Shanghai Composite Index fell 1.51 per cent.
Among European markets, Paris CAC 40 rose 0.36 per cent but Frankfurt's DAX shed 0.10 per cent in their morning deals. London's FTSE gained 0.36 per cent.
The US Dow Jones Industrial Average ended slightly higher by 0.06 per cent in Monday's trade.