Even as they jumped in, some investors said they weren't sure how long the rally would last, but the Dow Jones industrial average was on track to record its best week since the middle of June.
The Dow climbed 60 points to 13,600, its first time at that level since December 2007, the start of the Great Recession. Friday's gain put the Dow less than 600 points away from its all-time high, set in October 2007.
The Standard & Poor's 500 was up 10 to 1,470. The Nasdaq composite index was up 37 points, more than 1 percent, to 3,193, fueled by a jump in Apple, which set an all-time high.
Apple, the most valuable American company in history and the biggest stock in the S&P and Nasdaq, blew through $696 per share to an all-time high on the week that it released iPhone 5.
European and Asian stocks also spiked Friday in their first trading after the Fed move.
Investors are acutely aware of the economy's continuing problems. The stock market is steadily gaining while unemployment remains high and Europe trudges through a debt crisis.
Yet corporate profits remain high, and stocks are not expensive by historical standards compared with earnings.
Several investors said that the Federal Reserve, which touched off the rally Thursday when it announced it would take aggressive steps to try to boost the economy, was providing only a false sense of security.
They said investors were piling in because they believed the Fed would keep propping up the market, or because they wanted to capitalize on short-term euphoria over the Fed move.
Tyler Vernon, chief investment officer of Biltmore Capital in Princeton, N.J., compared the Fed action to "the morphine being pumped into the patient. It keeps the patient walking and talking."
"It's a scary time to be in the market because you're relying on stimulus measures four years into the recovery," he added.
The Fed pledged to buy more bonds, which could help the stock market by lowering bond returns and driving investors to stocks. It also promised to keep interest rates super-low through 2015, hoping to encourage borrowing and spending.
"How many times can you refinance your house?" said Jeff Sica, president and chief investment officer of SICA Wealth Management in Morristown, N.J.
The price of oil briefly rose above $100 for the first time since May, as unrest in the Middle East heightens concerns about the world oil supply. The Labor Department reported that gas drove up consumer prices in August by the most in three years.
Energy stocks were the best performers on the S&P 500, led by Valero Energy, Chesapeake, Chevron and others.
Among other stocks making moves:
— The Children's Place clothing store was up $1.86, or 3.2 percent, to $60.68 after a Citi analyst opened coverage of the company with a "buy" rating.
— The Cracker Barrel restaurant chain slipped $1.81, or 2.8 percent, to $64.36 after a KeyBanc analyst cut his rating to "hold" from "buy," citing high food costs.
— Staples was up 53 cents, or 4.4 percent, to $12.49 after Fortune magazine, citing anonymous sources, reported that private-equity firms are considering buying the office-supply company.