Dealers digested Chinese data pointing to a slight cooling in the world's second biggest economy, while the greenback picked up against major currencies after suffering a three-day sell-off last week.
Hong Kong rose 1.52 percent by the break, Seoul rose 0.77 percent and Singapore added 1.20 percent after figures showed the economy had grown at its strongest rate ever. Mumbai's Sensex was 0.65 percent up in early trade.
Australia, Tokyo, Shanghai, Wellington and Bangkok were closed for public holidays.
Castor Pang, research director at Cinda International in Hong Kong, predicted a strong start to the year for the markets.
"In the first half of 2011, I expect the US stocks to continue to do well on the economic recovery there, which should bode well for Asian stocks," he told Dow Jones Newswires.
"However, the (US) recovery is expected to be anaemic and once investors see that, there is likely to be a sharp (downward) correction."
Markets ended 2010 in a strong position, with most around two-year highs after clawing back losses suffered in the wake of the global financial crisis.
Dealers bought up stocks as sentiment was boosted by signs of an uptick in the United States, where unemployment looks to be subsiding as the world's economy picks up.
China on Saturday said manufacturing growth eased last month, suggesting attempts to cool the soaring economy could be working.
The country's Purchasing Managers Index fell to 53.9 from 55.2 in November, the China Federation of Logistics and Purchasing, which issues the data with the National Bureau of Statistics, said in a statement Saturday.
A figure above 50 indicates expansion while a figure below indicates contraction.
The figures confirm indications of a slowdown in a separate PMI from HSBC on Thursday, which fell to 54.4 in December from November's 55.3.
China has been struggling to calm the rapid growth of its economy, which posted annualised growth of 9.6 percent in the third quarter of 2010, slowing from 11.9 percent in the first three months.
The red hot pace of expansion has sent inflation to a two-year high of 5.1 percent and led Beijing to raise interest rates on December 25 for the second time in two months.
Singapore said its economy grew at a record 14.7 percent in 2010 as the export-dependent country bounced back from the global downturn.
The performance beat its previous best of 13.8 percent in 1970 and made the city-state Asia's best performing economy of the year.
The dollar strengthened against the euro and yen as traders backed the greenback after three days of selling.
A euro bought 1.3289 US dollars, down from 1.3381 in New York on Friday, and the US unit was at 81.35 yen from 81.28.
The European currency was changing hands at 108.11 yen from 108.32.
"There was a very strong three-day rally in the euro and it's quite normal to have short-covering," said Philip Wee, senior currency economist for DBS Group Research in Singapore.
The euro gained ground against the greenback in the last three days of 2010, driven partly by investors short-selling the dollar for the European currency.
Traders were also eyeing US Federal Reserve chairman Ben Bernanke's testimony on the US economic outlook to the Senate Budget Committee on Friday, Wee told AFP.
In the oil markets, New York's main contract, light sweet crude for delivery in February, rose nine cents to 91.47 dollars per barrel and Brent North Sea crude for February was up 14 cents at 94.89 dollars.
Gold opened at 1,416.00-1,417.00 US dollars an ounce in Hong Kong, up from Friday's close of 1,408.00-1,409.00 dollars.
In other markets:
-- Manila rose 0.33 percent, or 14.07 points, to 4,215.21.
Manila Electric surged 7.46 percent to 245 pesos amid reports of a network upgrade, while Metro Pacific, some of whose units are key shareholders in the utility, rose 6.68 percent to 4.15 pesos.