Nikkei soars 1.3%
Japan's benchmark Nikkei 225 finished at its highest level since June 8.
Banking shares were among the day's top performers, with Mitsubishi UFJ Financial Group and Sumitomo Mitsui Financial Group soaring 3.4 and 2.7 percent, respectively.
Honda Motor is in focus after the company's U.S. unit said Friday it has linked the death of a woman in Los Angeles last September to the rupture of a Takata airbag inflator, bringing the number of fatalities related to the defective airbags to eight.
Shares of the carmaker closed up 2.2 percent, while Takata sagged 0.4 percent.
Read MoreAsia's week ahead:All eyes on Greece
Kospi gains 0.4%
South Korea's key Kospi index extended gains into a four-day winning streak, thanks to a huge rally among blue chips and tourism-related counters.
The bourse's top two weighted stocks Samsung Electronics and Hyundai Motor jumped more than 1 percent each, while utility Kepco surged 4.8 percent on the back of news over the weekend that the state-run power firm will offer a temporary discount on its rates to households and small and medium-sized enterprises.
Consumer plays staged a comeback following recent losses due to the country's outbreak of Middle East Respiratory Syndrome (MERS). Major retailers Shinsegae and Lotte Shopping rallied 16.4 and 2.5 percent, respectively, while Hotel Shilla elevated 4.8 percent.
However, cosmetics makers AmorePacific gave up earlier gains to close down 0.3 percent.
Hang Seng rises 1.2%
Hong Kong's Hang Seng index notched up amid news that the city's bourse is consulting investors over current rules which ban dual-class shares. However, relatively cautious trading was observed with mainland markets closed for a national holiday.
Zijin Mining Group slumped nearly 3 percent after launching a bid for Australian gold explorer Phoenix Gold on Monday.
On Friday, the Shanghai Composite index tumbled 6.4 percent to settle at its lowest level since May 29, while chalking up its biggest weekly drop in seven years.
According to United Simsen Securities' Jackson Wong, a lack of pro-growth policies as of late sparked the steep correction: "Although there was disappointment when A-shares were excluded from MSCI's emerging market index, people weren't really concerned... but all of a sudden, we are lacking a lot of turnover because [Beijing] has not done anything in reaction to the weak economic data."
"They haven't done any reserve requirement ratio (RRR) or interest rate cuts , [as well as] any pro-growth policies, so I think that triggered a selloff because investors are tired of reports about high valuations," the associate director told CNBC.
While investors were likely anxious to see if the dramatic selloff will continue when markets reopen tomorrow, analysts say the technical pullback is healthy for mainland stocks in the long run.
If you look at the appreciation in Chinese markets so far, it's almost been a vertical rise since the beginning of this year, that is not sustainable. We were expecting a technical correction for quite some time now and finally, it's starting to happen," Audrey Goh, senior investment strategist at Standard Chartered, said. "We believe it's healthier for the markets in the long run to have a correction in the medium term."