The dollar held above the 105 yen mark after breaking it Tuesday for the first time since January, sparking a rally in Japanese exporters.
Tokyo rose 0.38%, or 59.75 points, to 15,728.35 while Hong Kong jumped 2.3%, or 568.93 points, to 25,317.95 and Shanghai rose 1%, or 22.58 points, to 2,288.63.
Seoul ended flat, dipping 0.38 points to 2,051.20 and Sydney was also a touch lower, easing 2.4 points to 5,656.10.
Data showed Australian economic growth slowed in the three months to June owing to a sharp fall in exports.
Mumbai closed up 120.55 points or 0.45% at 27,139.94 points and Kuala Lumpur's main index lost 2.82 points, or 0.15%, to 1,864.87.
Jakarta ended up 0.43%, or 22.55 points, at 5,224.135 and Singapore rose 0.62%, or 20.47 points, to 3,348.77.
Traders cheered a report from the Institute for Supply Management, which said Tuesday that a gauge of activity in the US manufacturing sector picked up pace in August, hitting its best level since August 2011.
"The parade of solid data continues," a Societe Generale analyst told Dow Jones Newswires. The figures are the latest suggesting the US economy is well on track to recovery and will add to pressure on the Federal Reserve to raise interest rates earlier than its timetable of next year.
The strong data "should keep upward pressure on the dollar, which will, in turn, make Japan stocks attractive", said SMBC Nikko Securities general manager of equities Hiroichi Nishi.
But US traders, returning to work Tuesday after the Labor Day weekend, were unimpressed. The Dow fell 0.19% and the S&P 500 slipped 0.07% although the Nasdaq added 0.39%.
Currency dealers shifted into the dollar, helping it breach 105 yen.
In afternoon Tokyo trade the greenback bought 105.06 yen compared with 105.10 yen in New York Tuesday afternoon.
The euro bought US$1.3135 and 137.88 yen against $1.3132 and 138.02 yen in US trade.
Buying was also supported by a jump in indexes measuring China's service sector.
HSBC said its services purchasing managers' index (PMI) hit a seven-month high of 54.1 last month, while the official PMI climbed for the first time in three months, to 54.4. A figure above 50 indicates growth and anything below points to contraction.
The results helped temper disappointment at Monday's manufacturing PMIs, which added to concerns about the world's number two economy.
Focus is now on central bank meetings in Japan and Europe, with a recent batch of soft economic data fanning calls for policymakers at both institutions to ease monetary policy to kickstart growth.
Friday also sees the release of a closely watched US jobs report that could add to growing pressure on the Federal Reserve to increase interest rates.