The Dow took the Fed ball and ran with it, crossing the finish line with a gain of more than 330 points.
Stocks had already been higher -- in fact, unusually high for a Fed meeting day -- after a better-than-expected service-sector report and oil's drop below $120 a barrel, but then got a big pop from the Fed.
The Dow Jones Industrial Average rose 331.62, or 2.9 percent, to close at 11615.77. The S&P 500 advanced 2.9 percent and the Nasdaq added 2.8 percent.
Financials blazed the trail, with the S&P financial-sector index advancing 5 percent, followed closely by consumer-discretionary stocks, which gained 4.5 percent.
The Fed's Open Market Committee held its target for interest rates at 2 percent, with one of the six members, Dallas Fed President Richard Fisher, dissenting, calling for a rate increase. (Read the Fed's statement.)
"The market seems to have reacted to the fact that there was only one dissenter," said Brian Gendreau, an investment strategist at ING Investment Management. "If there's only one dissenter, that pretty much suggests that the Fed is on hold," Gendreau said.
Economists and strategists largely agree the Fed will hold rates steady through year end. But, with the economy in a slowdown, next year could be a different story.
"I know a lot of forecasters looking for a slowdown in growth," Gendreau said. "I think there's a very good chance that we may need more Fed easing, more fiscal stimulus and another housing bill."
The Institute for Supply Management reported its gauge of service-sector activity rose more than expected to 49.5in July from 48.2 in June but remained below 50, indicating a second straight month of contraction. New orders declined but a measure of employment rose. And, on a day when the market is keenly focused on inflation, there was some relief as an index of prices paid fell by more than four points.
The service sector is a closely-watched gauge of the economy as it represents 80 percent of economic activity. This modest surprise was welcomed by the market.
Crude oil dropped more than $2 a barrel to settle at $119.17 a barrel, prompting speculation about how low it will go. The next stop will be $100 a barrel, according to technical analyst Nick Batsford from Hobart Capital.
Oil's drop has been a product of the sharp slowdown in global growth, Gendreau said, and he agrees we could be headed to $100 a barrel. If that happens, "consumers may start spending again," which would reignite growth, he said.
But be warned, it's not all up from here: "I'm not sure we've seen the bottom" in this market, Gendreau said. "We never had the complete bottom capitulation."
Thebig movers on the Dowtoday were AIG, Boeing & P&G.
AIG jumped 12 percent after UBS upgraded its rating on the stock to "buy" from "neutral," saying the company is well-positioned to weather future hits without raising additional capital. AIG reports earnings on Wednesday after the closing bell.
Boeing gained 6.3 percent as the the drop in oil prices boosted the energy-dependent aerospace giant.
Procter & Gamble rose 3.3 percent after the company beat earnings expectations as price increases and cost controls helped offset soaring prices for oil and other commodities. But the company, which makes everything from Pampers diapers to Olay skin-care products, warned that rising commodity costs will crunch margins in the new fiscal year, which began July 1.
In the financial sector, Lehman Brothers ismulling a sale of its investment-management division, which includes its Neuberger & Berman asset management unit as well as stakes in hedge funds and private equity funds, CNBC has learned. Its shares jumped 13 percent.
And Merrill Lynch CEO John Thain told CNBC that thebrokerage firm is "very well capitalized" but didn't rule out further writedowns if the value of risky assets continues to decline. Its shares rose 6.9 percent.
Goldman Sachs shares gained 1.6 percent, underperforming the rest of the sector, after Merrill cut its 2008 earnings estimates for Goldman and slashed its price target on the stock to $205, citing negative trends in some of the firm's strongest businesses.
Cablevision jumped 8.8 percent after the company announced that it is considering a spinoff of one or more divisions and other options to boost the company's struggling stock.
Still to Come:
WEDNESDAY: Mortgage applications; crude inventories; Earnings from Freddie Mac, Time Warner, Sprint Nextel and AIG
THURSDAY: Jobless claims; existing-home sales; consumer credit; Earnings from Barr Pharma, Toyota
FRIDAY: Productivity; wholesale trade; Earnings from Berkshire Hathaway
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