The rise appears to have been triggered by investors moving money from technology to industrial stocks.
According to preliminary figures, the Dow closed up 320 to 10,131. The Dow had risen by as much as 360 points since the opening bell.
The rise was not mirrored across other markets.
The Nasdaq composite index dropped 123 points to 4,583, and the Standard & Poor's 500 index was up 33 to 1,392.
Old-line industrial companies like DuPont, Johnson & Johnson, and 3M, powered the Dow's rise -- quite a reversal from last week, when these "dinosaur" firms were shunned by investors worried about interest rate hikes.
High-tech companies on the Nasdaq, such as Yahoo! and PMC-Sierra, were mostly lower, compounding the index's 341-point loss in the past two sessions.
Traders said the market's continued volatility suggested that investors were reluctant to take major new positions in the days ahead of the government's reports on the Producer Price Index (PPI) and the Consumer Price Index (CPI).
The PPI, due for release Thursday, and the CPI, due out Friday, are closely watched gauges of inflationary pressures.
The Federal Reserve is expected to take both reports under consideration when it meets next Tuesday to discuss interest rates.
Many on Wall Street expect the Fed to raise rates. An increase would be the fifth since last June, when the Fed began trying to engineer a gradual slowdown in the economy to prevent inflation.