The Shanghai Composite was turbo-charged on Monday and jumped 4.7 percent higher, its biggest daily gain since January 21.
Shanghai stocks are up almost 50 percent so far this year.
The sister Shanghai-Shenzhen CSI 300 index also popped 4.86 percent higher, its best day in two and a half years.
Hong Kong-listed shares in Chinese broker Huatai, the biggest IPO in Asia so far this year, opened flat but gained 4.4 percent on its first day of trading .
Japan's Nikkei turned positive in afternoon trading and extended its gains to twelve days. This is the longest winning streak for Japan's benchmark index since February 1998.
In contrast, Australia's ASX 200 opened the day lower and ended down 0.70 percent and Seoul's Kospi fell 0.63 percent.
Little action was seen on the major currency pairs. The Japanese yen was quoted at around 124.10 and the Australian dollar at about 0.7651 against the U.S. dollar throughout the day.
Earlier in the day, China's official manufacturing PMI came in at 50.2, in line with forecasts, and rose slightly from April's 50.1.
The services PMI fell slightly, to 53.2, from 53.4 in April.
A little later, the China final HSBC PMI was released: at 49.2, the indicator suggests China factory activity fell for the third straight month.
The 50-mark demarcates expansion from contraction.
Financial markets in Singapore, Thailand and New Zealand were closed on Monday for public holidays.
Last Friday, the Dow Jones industrial average ended about 115 points lower after falling more than 150 points during the session, although it still posted a 0.95 percent gain for May. After rallying for the week, the U.S. dollar and Treasuries traded flat on Friday.
Greece will be back at the top of global investors' radars this week. The Greek government, elected on an anti-austerity platform, is saying it hopes to reach a reform-for-rescue deal with its international bailout creditors this week, according to Reuters.
A 300 million euro payment is due to the International Monetary Fund on June 5.
--See Kit Tang and Evelyn Cheng contributed to this article.