But the dollar took another slide against the yen, which hurts Asian exporters, and some analysts said it won't take long for local concerns to override the benefits of America's moves.
There also was a strong rally in European stocks on Friday. Leading European bourses traded around two percent higher after overnight surges in Asian and American markets. Gold pushed back through the key $300 an ounce level.
CBS News Correspondent Barry Petersen reports that Japan led the way with the Nikkei closing up over 2 percent. That wasn't bad, but, compared to the rest of Asia, it was lagging.
Hong Kong shot up 9 percent to its highest close since March. Singapore did better, with more than a 9 percent increase. Bruised and battered Thailand ended with an 8 percent gain.
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"External problems may be eased by the U.S. rate cut, but the problems remain with Japan's domestic economy," said Kenji Karikomi, a general manager at Daiwa Securities in Tokyo.
Across the board Thursday, the United States provided Asia's rattled and depressed markets with one good sign after another.
For the second time in about two weeks, the U.S. Federal Reserve cut interest rates by a quarter-point. The surprise reductions ignited an explosive rally on Wall Street. The Dow Jones industrial average ended the day up 330.58 points, or 4.2 percent, its third-biggest point gain in history.
American economists also speculated that more rate cuts are imminent as the central bank tries to keep global economic turmoil from dragging the United States into a recession.
In Singapore, the Straits Times Index rose 94.85 points, or 9.2 percent, to close at 1,119.6.
In Hong Kong, the blue-chip Hang Seng Index rose 806.59 points, or 8.9 percent, to close at 9,777.01 points, its highest level since May 11.
Investors hoped that the territory's banks would once again follow the U.S. lead and reduce interest rates, too. And it turned out they were right. Moments after the market closed, banks cut the deposit rate, a key lending rate in Hong Kong.
Property stocks led the index, posting a 13.5 percent gain.
The surge in volume indicated that cash-rich institutional investors are returning to the market, said Howard Gorges, director of South China Securities Ltd. in Hong Kong.
In Tkyo, following three days of declines, the benchmark Nikkei Stock Average of 225 issues gained 285.17 points, or 2.2 percent, to close at 13,280.54.
The Japanese got an extra dose of good news Friday - Parliament's upper house gave final approval to the last bills bailing out failing banks, part of a plan to prime the pump by injecting money into the economy.
While Japanese citizens may be relieved the bank crisis is being resolved, they are not overly happy at the managers who got the banks nto the mess.
The world can take heart that Japan is making those major steps to get its fragile economic house in order. That should help markets everywhere.