Weaker-than-forecast US jobs figures raised concerns about the world's number one economy but also fuelled hope that the Federal Reserve will hold off winding down its stimulus programme for the time being.
The SET index surged 3.60%, or 48.06 points, to 1,384.31. Jakarta climbed 2.92%, or 118.90 points, to 4,191.26, Kuala Lumpur gained 1.35%, or 23.23 points, to 1,747.03, Manila rose 0.38%, or 22.42 points, to 5,997.04, and Singapore gained 1.31%, or 39.85 points, to 3,088.20.
Elsewhere, Tokyo rose 2.48%, or 344.42 points, to 14,205.23. Japanese dealers bought into construction and real estate after Tokyo's Olympics success, while there was also cheer for better-than expected gross domestic product data for the April-June quarter.
Shanghai soared 3.39%, or 72.53 points, to 2,212.52 and Hong Kong added 0.57%, or 129.43 points, to 22,750.65. Seoul closed 0.99% higher, adding 19.36 points to 1,974.67.
Chinese data on Sunday showed exports jumped 7.2% year-on-year to US$190.6 billion last month, much better than the 6% expected by economists. It was also better than the 5.1% rise seen in July.
The figures are the latest in a string of good results out of Beijing that indicate China's painful slowdown over much of the first six months of 2013 may have come to an end. Earlier this month the government said manufacturing activity grew at its fastest pace in 16 months in August.
Investors were cheered by the news because Chinese growth is key to helping drive the economies of many other countries in the region.
Tokyo dealers were already in buying mood after the Olympics result when data was unveiled showing the Japanese economy grew 0.9% over the previous quarter in April-June, up from a preliminary reading of 0.6%.
On an annualised basis the economy expanded 3.8%, the government said, up from the first estimate of 2.6%. Annualised figures show the rate of growth if the data was stretched across an entire year.
"The Olympics, better-than-expected China's export data, and strong GDP data are all supporting the market today," Haruhiko Kuramochi, strategist at Mizuho Securities, told Dow Jones Newswires.
The Nikkei was also supported by a weaker yen as confidence in the global economy saw investors move into higher-risk assets looking for better returns.
Emerging markets - especially in emerging economies - were hammered last month as foreigners fled back to the West in expectation the Fed will start to cut back on its vast bond purchases by the end of the year.
While buying sentiment was strong, an ongoing dispute between Russia and the United States over Syria had dealers on edge as presidents Barack Obama and Vladimir Putin failed Friday to reach agreement at a G20 summit on how to deal with the crisis.
US Secretary of State John Kerry said in London on Monday that Syrian President Bashar al-Assad could prevent a US-led attack if he turned over his chemical weapons in the next week.
But Mr Kerry told a press conference in London that he had no expectation that Mr Assad would give up the arms.
The US top diplomat was asked if there was anything that the Syrian government could do or offer now to prevent a military strike.
"Sure, he could turn over every single bit of his chemical weapons to the international community in the next week - turn it over, all of it, without delay and allow a full and total accounting for that," Mr Kerry told reporters.
"But he isn't about to do it and it can't be done."
The US has the full support of Britain on Syria despite the fact that London will not join military action, British Foreign Secretary William Hague said on Monday.
Speaking after talks with Mr Kerry in London, Mr Hague told a news conference: "They have the full diplomatic support of the United Kingdom" adding that Britain would be "working closely with our closest ally" on Syria.
But the American public strongly opposes a US military intervention in Syria, despite a majority believing that Mr Assad's regime gassed its own people, a poll showed Monday.
Almost six in 10 of the 1,022 adults questioned - 59% - said Congress should not pass a resolution authorising even limited military action against Syria, a CNN/ORC International poll found.
More than seven in 10 said any such strike would not achieve significant US goals or serve US national interests.
And even if Congress authorises military action against Syria, a 55% majority would still oppose air strikes against Syrian military targets. Without congressional support, the opponents increased to 71% of respondents.
However, most of those questioned - 57% - said their representative's vote in Congress would not make a difference in how they voted in upcoming 2014 mid-term elections. The mid-term polls are usually dominated by domestic issues.
The poll comes at the start of a crucial week for Mr Obama, who is set to make a round of interviews with six major television news outlets later Monday as he seeks to convince the American public and reluctant lawmakers.
On Tuesday, the president will travel to Capitol Hill to press lawmakers in person just hours before he addresses Americans from the White House, ahead of a possible Senate vote on authorising force in Syria later this week.
The CNN poll had a sampling error of plus or minus three percentage points.