Buoyancy in global markets and a strengthening rupee further propped up sentiment, traders said.
Investors also cheered regulatory approval for human trials of another potential COVID-19 vaccine.
After touching a high of 36,110.21, the 30-share BSE Sensex settled 177.72 points, or 0.50 per cent, higher at 36,021.42.
The NSE Nifty rose 55.65 points, or 0.53 per cent, to end at 10,607.35.
This is the highest closing for both the benchmarks since March 6.
During the week, the Sensex advanced 850.15 points or 2.41 per cent, while Nifty gained 224.35 points or 2.16 per cent.
Bharti Airtel was the top gainer in the Sensex pack on Friday, rallying 4.05 per cent, followed by Bajaj Auto, TCS, Titan and HCL Tech.
Index heavyweight Reliance Industries spurted 1.53 per cent after the company said Intel Capital will buy 0.39 per cent stake in Jio Platforms for Rs 1,894.50 crore.
Intel Capital is 12th company to join the list of marquee firms who have picked up stake in Jio Platforms, taking the total investment amount to Rs 1,17,588.45 crore.
On the other hand, IndusInd Bank, Tata Steel, HDFC Bank and Bajaj Finance were among the laggards, shedding up to 1.50 per cent.
Zydus, part of the Cadila Healthcare group, on Friday said its indigenously developed COVID-19 vaccine candidate -- ZyCoV-D -- has successfully completed pre-clinical phase and has received permission from Indian authorities to conduct human trials.
This comes just a day after Germany's BioNTech and US pharmaceutical giant Pfizer reported positive preliminary results from a joint project for a potential COVID-19 vaccine.
Domestic indices also took cues from Asian peers that followed overnight gains on Wall Street after positive jobs data release in the US, traders said.
"Markets during the week moved higher on hopes of a COVID-19 vaccine coming to everyone's rescue earlier than expected. Bourses across the world are also riding on early availability of a vaccine inspite of unstable economic growth.
"Another round of shutdowns in a few countries is frightening but hopes of a drug/ vaccine are keeping markets upbeat. A peculiar historic trend during bull market tops is observed currently," said Jimeet Modi, Founder and CEO, SAMCO Securities & StockNote.
BSE telecom, power, capital goods, teck, energy and industrials indices rallied up to 3.45 per cent, while metal, bankex, finance and basic materials slipped in the red.
Broader BSE mid-cap and small-cap indices rose up to 0.56 per cent.
Bourses in Shanghai, Hong Kong, Tokyo and Seoul ended on a positive note, while those in Europe opened in the red.
Meanwhile, international oil benchmark Brent crude futures fell 1.69 per cent to USD 42.41 per barrel.
On the currency front, the rupee appreciated 38 paise to settle at 74.66 against the US dollar.
The number of COVID-19 cases around the world has crossed 1.08 crore and the death toll has topped 5.20 lakh.
In India, the number of infections has touched 6.25 lakh, with over 18,000 fatalities. ANS ABM ANS ABM ABM