NEW YORK—The government’s latest bailout of a big financial company—this time, Citigroup Inc.—sent Wall Street soaring Monday for the second straight session as investors bet that the worst of the financial industry’s problems might finally be over. The Dow Jones industrials soared nearly 400 points, while all the major indexes jumped more than 4.5 percent.

The surge gave the market its first two-day advance since the end of October and the Dow its biggest two-day percentage gain since October 1987, the month of the Black Monday crash. The Dow’s 891-point rise over the two sessions...

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