The broader Nifty too breached the 9,600-level, also in a first, before settling at a record high of 9,595.10.
Sustained buying, both by domestic and foreign investors, propped up the market at elevated levels amid optimism for more reforms by the government.
The BSE Sensex has risen 25.53 per cent, while the NSE Nifty has gained 30.38 per cent since the BJP-led NDA government came to power in May 2014.
Creation of new positions by participants following the beginning of the June futures and options (F&O) series added to the momentum, brokers said.
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After paring some gains, the 30-share index settled at 31,028.21, up 278.18 points, or 0.90 per cent. It surpassed the earlier record closing of 30,750.03 hit yesterday.
It was the third straight week of gains for the key indices. The Sensex rose by 563.29 points, or 1.84 per cent, while the Nifty finished the week 167.20 points, or 1.77 per cent higher.
"Market touched another milestone supported by continued buying interest on index heavyweights post expiry. Expectation on good monsoon and a slow pace in interest rate hike by US Fed continue to weigh on the sentiment.
Foreign institutional investors bought shares worth a net Rs 589.11 crore on Thursday, which added to the upbeat sentiment.
Tata Steel soared 5.46 per cent to emerge as the biggest Sensex gainer, followed by ITC Ltd at 2.99 per cent on encouraging fourth quarterly earnings.
Other big gainers were Power Grid (2.57 per cent), Reliance Industries (2.53 per cent), Adani Ports (1.82 per cent), Asian Paints (1.76 per cent), Infosys (1.46 per cent), Maruti Suzuki (1.30 per cent), ICICI Bank (1.28 per cent), Bharti Airtel (1.12 per cent), Tata Motors (1.11 per cent), M&M (1.11 per cent), L&T (1.05 per cent), Axis Bank (1 per cent), ONGC (0.95 per cent) and Coal India (0.90 per cent).
Sectorwise, BSE metal index gained the most by rising 3.40 per cent, followed by oil&gas 2.08 per cent, FMCG 1.77 per cent, power 1.61 per cent, consumer durables 1.56 per cent, capital goods 1.47 per cent, auto 1.34 per cent, PSU 1.13 per cent and banking 0.78 per cent.
Buying activity in the broader markets also gathered momentum, with the mid-cap index surging 2.06 per cent and small-cap index gaining 1.60 per cent.
European markets were in the red in their early deals. Paris CAC 30 fell 0.70 per cent and Frankfurt's DAX lost 0.41 per cent. London's FTSE, however, was marginally up by 0.10 per cent.