The U.S. debt drama has also heightened speculation of the Federal Reserve delaying the start of its stimulus reduction plan, underpinning riskier assets but keeping the dollar pinned down to an eight-month low.
MSCI's broadest index of Asia-Pacific shares outside Japan advanced 0.5 percent to a five-month high, adding to a 0.6 percent rise in the previous session.
Investors were relieved after data showed China's economy grew 7.8 percent in the third quarter, its fastest pace this year and in line with expectations, as firmer foreign and domestic demand lifted factory production and retail sales.
Still, the reaction across Asia to the data was somewhat muted by the uncertainty about the outlook for global demand, underlined by a surprise fall in China's September exports.
China's CSI300 index ticked up 0.3 percent.
"The Q3 GDP figure is in line with market expectations but the uncertainty is whether the current recovery is sustainable," said Shen Jianguang, chief China economist with Mizuho Securities in Hong Kong.
Overnight, the U.S. Standard & Poor's 500 index closed at a record high. U.S. S&P E-mini futures added 0.2 percent in Asian trade on Friday, indicating a further rise when Wall Street opens later in the day.
U.S. Democrats and Republicans reached an 11th-hour agreement on Wednesday to break an impasse, pulling the world's largest economy from the brink of an historic debt default as the deal funds the government until Jan. 15 and raises the borrowing limit through to Feb 7.
Analysts said economic weakness resulting from the 16-day shutdown and uncertainty over the next round of budget and debt negotiations may keep the Fed from withdrawing monetary stimulus at least until a few months into next year.
A simple estimate suggested the direct and indirect impact of the shutdown would weigh on the annualized fourth-quarter gross domestic product growth by 0.4 percentage point, Morgan Stanley said.
In September, the Fed stunned markets by opting to delay trimming its $85 billion-a-month bond purchases. Stimulus tapering expectations have now been pushed down to December.
"The U.S. dollar is the worst performing currency as attention shifts from the U.S. debt debacle to incoming Fed rhetoric, and bond markets may be leading the way," said Christopher Vecchio, currency analyst at DailyFX.
"The U.S. Treasury yield curve continues to flatten, which typically occurs when either slower economic growth is expected and/or additional monetary easing is forecasted," he added.
Yields on benchmark 10-year U.S. Treasuries hit a two-week low on Thursday at 2.581 percent. They were quoted at 2.603 percent in the Asian session.
The dollar held steady at 98.065 yen after shedding 0.8 percent against the Japanese currency overnight to log its biggest one-day percentage drop in a month, while Tokyo's Nikkei average was flat, under-performing regional markets.
The greenback also lost more than 1 percent against the euro on Thursday. The dollar was steady near an eight-month low at $1.36625 to the euro in Asian trade on Friday.
Against a basket of major currencies, the dollar ticked up 0.1 percent, stabilizing after hitting an eight-month trough on Thursday.
"The Fed's taper decision will ultimately be tied to the economic data - which have been hard to come by since the government shutdown," analysts at Barclays Capital said in a note.
In the coming week, investors will get a slew of U.S. economic data that had been delayed by the shutdown.
All eyes will be on the crucial non farm payrolls report next Tuesday. The report was originally scheduled for release on Oct. 4.
"The bias now is for the whole Fed cycle to be re-repriced towards a later exit and slower tightening," analysts at Societe Generale wrote in a note. "The bias is thus for short-term U.S. dollar forward rates...to go even lower. This will do the U.S. dollar no favors in the near term."
Among commodities, gold took a breather after rallying almost 3 percent overnight - its biggest one-day rise in a month - as the dollar weakened. It was down 0.1 percent at about $1,318 an ounce, though not far from a more than one-week high reached on Thursday.
U.S. crude prices held above $100 a barrel, having fallen to their lowest level in more than three months in the previous session as stockpiles in oil hub Crushing began to reverse a months-long decline, and as signs of progress in talks over Iran's nuclear programme also pressured prices.