Australia's main index led the way with a gain of 0.5%, while MSCI's broadest index of Asia-Pacific shares outside Japan added 0.16%.
Markets in Seoul and Hong Kong are also off on Tuesday to celebrate the Buddha's birthday.
Sentiment did get a fillip after the Institute for Supply Management's US services sector index rose to 55.2 in April, the fastest pace in eight months and easily topping forecasts. A reading above 50 indicates expansion.
The data added to evidence that the US economy is emerging from a particularly harsh winter-induced slowdown and provided a welcome offset to worries about China.
"The US is showing signs of recovering from particularly slow momentum in Q1, driven to a significant extent by adverse weather effects, and the euro area remains on a stable, gradual upward trajectory," noted analysts at Barclays.
"In Japan, the sales tax hike frontloading and payback, which began last month, were largely in line with expectations."
The better US news helped Wall Street recover early losses. The Dow closed up 0.11%, while the S&P 500 gained 0.19% and the Nasdaq 0.34%.
MSCI's all-country world stock index traded flat, while the euro zone's blue-chip Euro STOXX 50 index pared some losses to close 0.21% lower.
Bonds took the opposite tack with Treasuries surrendering some of the gains made last week. Yields on 10-year paper lurched up to 2.61%, having been as low as 2.57%.
The US Treasury auctions three-, 10- and 30-year debt this week which will be a useful litmus test of investor demand.
In currency markets, trading was subdued as holidays in London and Tokyo sapped liquidity. The dollar index was steady at 79.501, having drifted between 79.433 and 79.527 on Monday.
The euro stood at $1.3875, having hugged a tight $1.3864-$1.3887 range. Against the yen, the greenback was little changed at 102.15 as was the euro at 141.71.
There was little in the way of major economic data scheduled for Asia on Tuesday, leaving attention on the outcome of Australia's central bank policy meeting at 0430 GMT.
The Reserve Bank of Australia (RBA) is considered almost certain to leave its cash rate unchanged at 2.5% and maintain a steady policy outlook.
Many, however, will be looking for any commentary on the level of the Australian dollar, which has remained stubbornly high. The Aussie was last at $0.9278, holding above support at $0.9250.
In commodities, gold was firm at $1,310.71 an ounce after touching three-week highs, partly due to the simmering tensions in Ukraine.
Pro-Russian rebels shot down a Ukrainian helicopter in fierce fighting near the eastern town of Slaviansk on Monday, and Kiev drafted police special forces to the southwestern port of Odessa to halt a feared spread of rebellion.
Loss of control of Odessa would be a huge economic and political blow for Ukraine, a country the size of France that borders several NATO countries and aspires to join the military alliance, a primary source of concern for the Kremlin
Oil prices extended their recent decline. Brent crude for June delivery was off 8 cents at $107.64 a barrel, while US crude eased 2 cents to $99.46 a barrel.