NEW YORK—An already soaring Wall Street extended its advance Tuesday after the Federal Reserve left interest rates unchanged and assuaged some of the market’s fears about the economy. The Dow Jones industrial average shot up more than 330 points, and all the major indexes had gains approaching 3 percent.

The market was enjoying a big rally before the Fed meeting as investors responded to a report that services sector activity fell less than expected last month and to another drop in oil prices that took crude as low as $118 a barrel.

The Fed gave stocks another huge pus...