NEW YORK—Wall Street soared for the second straight day Wednesday, rallying in the last hour of trading after a rebound in financial stocks and optimism about private sector jobs helped investors brush off a sharp jump in oil prices. The Dow Jones industrials rose more than 180 points, bringing its two-day gain to more than 450.

Bank and brokerage stocks, many trading at multi-year lows, turned higher and led the late advance. There was some relief in the market after the Federal Reserve said it would extend and expand its emergency borrowing program for investment banks. The centr...