The NSE Nifty too breached the 11,500-level with a jump of 145.30 points.
All sectoral indices ended in the green, led by realty, power, consumer durables and metals.
Brokers said sentiment was bullish on continuous recovery in the rupee amid reports that the government may announce steps to prop up the domestic unit.
Prime Minister Narendra Modi will hold meetings with top officials Friday and Saturday to review the economic situation.
The rupee strengthened by another 65 paise to 71.53 (intra-day) against the dollar Friday, also supported by a fall in crude oil prices.
Domestic cues were positive after official data released after trading hours Wednesday showed that industrial production (IIP) grew at 6.6 per cent in July, while retail inflation cooled to a 10-month low of 3.69 per cent in August.
Meanwhile, WPI inflation also eased to a four-month low of 4.53 per cent in August on softening prices of food articles, especially vegetables.
The benchmark BSE Sensex stayed in the positive terrain through the session and touched a high of 38,125.62. It finally settled 372.68 points, or 0.99 per cent higher at 38,090.64 — its highest closing since September 7 when it had finished at 38,389.82.
Also, the broader Nifty climbed 145.30 points, or 1.28 per cent to finish at 11,515.20. Intra-day, it shuttled between 11,523.25 and 11,430.55.
However, the indices closed with losses for the second straight week. The Sensex lost some 300 points, or 0.77 per cent, while the NSE Nifty fell 73.90 points, or 0.64 per cent, during the week.
Meanwhile, domestic institutional investors (DIIs) remained net buyers, picking up shares worth Rs 541.44 crore on Wednesday. However, foreign portfolio investors (FPIs) sold equities to the tune of Rs 1,086.39 crore, provisional data showed.
“Ease in inflation and recovery in rupee added optimism in the market. Stability in yield and rupee will be crucial for the market momentum while investors have continued to stay cautious due to global triggers.
“The global peers also traded on a positive note in expectation of ease in trade tensions between US and China. Any redressal in tensions will provide enough headroom for domestic market,” said Vinod Nair, Head of Research, Geojit Financial Services.
The overall investor optimism rubbed off on broader markets as well, lifting the BSE mid-cap and small-cap indices by 1.62 per cent and 1.38 per cent.
Vedanta was the big hitter in the Sensex kitty, surging 5.25 per cent after the company said Thursday it has discovered natural gas in a Krishna Godavari basin block.
PowerGrid, Asian Paints, NTPC, Yes Bank, HDFC Ltd, IndusInd Bank, ONGC, Sun Pharma, Bharti Airtel, SBI, Tata Steel, ICICI Bank, Maruti Suzuki, Tata Motors, M&M, Adani Ports, TCS, Hero MotoCorp and L&T were among the other gainers, rising by up to 3.31 per cent.
Only Infosys and Coal India finished with losses.
Sectorally, BSE realty advanced 3.29 per cent, followed by power 2.55 per cent, metal 2.26 per cent, consumer durables 2.26 per cent, utilities 2.26 per cent, PSU 2.22 per cent, oil and gas 2.09 per cent, healthcare 1.91 per cent, infrastructure 1.82 per cent, finance 1.70 per cent, telecom 1.63 per cent, banking 1.20 per cent, auto 1.18 per cent, energy 0.83 per cent, capital goods 0.82 per cent, FMCG 0.59 per cent and teck 0.17 per cent.
Fertiliser stocks were back in demand after the cabinet approved a Rs 15,053 crore new procurement policy to ensure remunerative prices to farmers.
Shares of sugar companies jumped as much as 20 per cent after the government raised ethanol price for blending in petrol by 25 per cent in a bid to cut surplus sugar production.
Simbhaoli Sugars, Rana Sugars, Magadh Sugar & Energy, Rajshree Sugars & Chemicals, K M Sugar Mills, Avadh Sugar & Energy, among others, ended higher.
Globally, most Asian shares closed up on reports of talks between the US and China to resolve their trade dispute, while Europe too rose in early deals.
Japan’s Nikkei spurted 1.20 per cent, while Hong Kong’s Hang Seng gained 0.97 per cent. Shanghai Composite, however, shed 0.18 per cent.
In the Eurozone, Frankfurt’s DAX rose 0.59 per cent and Paris CAC 40 climbed 0.58 per cent. London’s FTSE edged up 0.42 per cent.