Japan's Nikkei 225 index edged up 0.3% to 21,343.09 after the government reported Monday that the economy grew at a better-than-expected 2.1% annual pace in January-March.
In Australia, the S&P ASX 200 rose 1.7% to 6,471.80, boosted by a shock election victory for Prime Minister Scott Morrison. His conservative government looked set to form a majority government, leaving bewildered voters wondering how they were taken by surprise since the opposition Labor Party had been expected to win.
Voting in India's election, which lasted more than five weeks, ended with exit polls predicting Prime Minister Narendra Modi's Hindu nationalist party and its allies will win another five years in office.
The election has been seen as a referendum on Modi and his Bharatiya Janata Party, whose main opposition is the Congress party, led by Rahul Gandhi, the scion of the Nehru-Gandhi dynasty that has produced three prime ministers.
The outcome appeared to please investors, as the benchmark Sensex added 2.4% to 38,834.49.
But markets in Shanghai and Hong Kong fell back in the absence of any positive updates on the trade standoff between the U.S. and China.
The Shanghai Composite index lost 0.6% to 2,865.25 while Hong Kong's Hang Seng index slipped 0.4% to 27,827.
Elsewhere in Asia, South Korea's Kospi added 0.5% to 2,065.71 and shares rose in Taiwan and Indonesia. Markets were closed in Thailand, Malaysia and Singapore for public holidays.
ENERGY: Benchmark U.S. crude picked up 85 cents to $63.61 per barrel in electronic trading on the New York Mercantile Exchange. It lost 11 cents to $62.76 per barrel on Friday. Brent crude, the international standard, climbed 99 cents to $73.20 per barrel.
CURRENCIES: The dollar rose to 110.22 Japanese yen from 110.08 yen on Friday. The euro weakened to $1.1154 from $1.1161.