Casting aside any hesitation about an aggressive interest rate cut, investors sent stocks soaring to their highest gains in five years on Tuesday as shares of financial firms surged in the hopes that the Federal Reserve has finally taken hold of the credit crisis. The Dow Jones industrial average gained 420 points.

The surge began at the opening bell after two big investment banks, Lehman Brothers and Goldman Sachs, delivered stronger-than-expected earnings. It faltered only briefly after the Fed’s announcement in the afternoon that it would cut its benchmark interest rate by three-quarters of a point, with the Dow tacking on nearly 300 points in the final hour and a half.

At the end of trading, the Dow was at 12,392.66, a gain of 420.41 points, or 3.51 percent. The Standard & Poor’s 500-stock index advanced 4.24 percent, its best performance since October 2002. It was up 54.14 points, to 1,330.74. The Nasdaq composite index also gained 4.2 percent, or 91.25 points, to 2,268.26.

The rally capped a week of extraordinary efforts on the part of the central bank to restore confidence to financial markets after the near collapse of Bear Stearns, one of Wall Street’s most venerable investment banks.