The wider NSE Nifty too went past the 10,550-level.
A firming trend on Asian and European bourses following a good show by Wall Street on Friday bolstered sentiment.
The 30-share BSE Sensex opened on a strong footing at 34,225.72 and maintained its upward trend to hit the day's high of 34,483.39 before ending at 34,445.75, up 303.60 points, or 0.89 per cent.
This level was last seen on February 5, when the Sensex had closed at 34,757.16.
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The Nifty finished the day at 10,582.60, showing a hefty gain of 91.55 points, or 0.87 per cent, after shuttling between 10,592.95 and 10,520.20.
Gains were led by realty, auto, capital goods, banking, infrastructure, metals, power, oil & gas, PSU and consumer durables sectors, which rose up to 3.30 per cent.
Domestic institutional investors (DIIs) net bought equities to the tune of Rs 1,514.03 crore, while foreign portfolio investors (FPIs) sold shares worth Rs 486.32 crore on Friday, provisional data showed.