Shanghai Comp up 1.6%
China's Shanghai Composite index finished at a one-week high amid a three-day winning streak, thanks to the central bank's interest rate cut on Sunday.
Brokerage houses led advances, with Founder Securities and Haitong Securities closing up 2.3 and 1.5 percent, respectively.
While Industrial and Commercial Bank of China failed to capitalize on Monday's rally and closed down 0.2 percent, other financial plays finished in the black with modest gains. In the property space, heavyweight developers like Poly Real Estate and China Vanke tumbled more than 1 percent each.
Automakers were mixed following data that showed China's auto sales fell 0.5 percent on-year in April. While SAIC Motor and Guangzhou Auto retreated 0.7 and 1.4 percent, respectively, Dongfeng Auto charged up by the daily maximum allowable of 10 percent. Shenzhen-listed FAW Group bounced up nearly 2 percent, but Changan Automobile Group declined 2.4 percent.
Meanwhile, Hong Kong markets took a breather and ended down 1.1 percent.
Read MoreChina faces 'enormous challenges': Paulson
ASX gains 0.9%
Australia's S&P ASX 200 index finished in the black for the first time in a week, ahead of the nation's annual federal budget due later in the day, which markets expect to show a deficit of over 40 billion Australian dollars ($31.5 billion).
Banks were in the spotlight as National Australia Bank resumed trading after announcing a mammoth $5.5 billion rights issue last Thursday. Shares of the lender closed down 0.5 percent as it played catchup in a technical correction, analysts say. Marking a comeback following last week's rout due to downbeat earnings, Australia and New Zealand Banking, Westpac and Commonwealth Bank of Australia elevated between 0.9 and 1.5 percent.
The resources space turned higher in the afternoon session, with market bellwether BHP BIlliton outperforming the sector with a rise of 2.2 percent. "China has really given some of these materials plays some renewed vigor. However, these moves could well be a flash in the pan and might not necessarily go the distance," Stan Shamu, IG's market strategist, wrote in a note.
Qantas was among the top gainers for Tuesday, raking in its highest gain since September 2008 by soaring 7.2 percent, after CEO Alan Joyce said lower fuel bill to boost the airline's transformation plan.