Japan's benchmark Nikkei 225 was up 1.11 percent, the broader Topix gained 1.19 percent, South Korea's Kospi added 0.43 percent, while Hong Kong's Hang Seng index lost 0.56 percent.
Chinese markets mostly shrugged off a lower-than-expected reading of the Caixin Services PMI, with the Shanghai composite up 0.17 percent and the Shenzhen composite adding 0.78 percent.
Down Under, the S&P/ASX 200 closed up 59.87 points, or 1.19 percent, at 5,081.10, boosted by gains in the financials, energy, and materials sectors - up 1.78, 1.15 and 1.98 percent, respectively.
Angus Nicholson, a market analyst from IG, said in an afternoon note that the resurgence in commodities prices, from oil to industrial metals, appeared to underpin the positive moves in equities.
He added the rally could find near term support from a series of important events due to take place in the coming days. These include the upcoming U.S. non-farm payrolls report on Friday, China's National People's Congress (NPC) that begins this weekend , as well as European Central Bank and Bank of Japan meetings next week.
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