American stocks rallied, sending the Dow Jones Industrial Average and Nasdaq Composite Index to their biggest gains this year, after International Business Machines Corp.’s earnings beat forecasts.

IBM, the world’s biggest computer-services provider, rose the most in five years in New York Stock Exchange trading and triggered the steepest advance in technology shares since November. Newmont Mining Corp., the world’s second-largest gold miner, and Halliburton Co., the second-biggest oilfield services company, gained as gold and oil advanced, helping the market rebound from three straight weeks of losses.

The Standard & Poor’s 500 Index, off to its worst start for a year since 1991, added 15.23, or 1.1%, to 1,416.25. The Dow average rose 171.85, or 1.4%, to 12,778.15. The Nasdaq Composite increased 38.36, or 1.6%, to 2,478.3.

“The IBM news is a welcome relief to a market that’s under pressure,” a manager of $11 billion at Security Global Investors in Irvington, N.Y., Mark Bronzo, said. “Hopefully IBM sets the tone that we’re going to hear from a lot of other companies, that earnings are going to be OK.”

Higher profits from computer companies may limit a broader decline in earnings in the fourth quarter as financial companies write off more losses from investments linked to subprime mortgages. Technology companies in the S&P 500 are forecast to post average profit growth of 22% in the final quarter of 2007, compared with a drop of 10% in the entire index, according to a Bloomberg survey January 11.

IBM gained $5.26, or 5.4%, to $102.93, accounting for about a quarter of the Dow average’s advance. Sales rose to $28.9 billion in the fourth quarter, the company said in a statement of preliminary results, helped by growth in Asia, Europe, and developing countries. That topped the $27.7 billion average of analysts’ estimates compiled by Bloomberg. Profit from continuing operations climbed to $2.80 a share, also beating projections.

Apple Inc. added $6.09 to $178.78. The company’s 2008 earnings may climb to $5.04 a share on sales of $31.7 billion, Bank of America analysts led by Scott Craig wrote in a research note. Craig’s previous estimates were $4.87 a share and $30.7 billion, respectively.

The chief executive officer, Steve Jobs, may unveil new products at the company’s annual Macworld conference tomorrow in San Francisco, including a slimmed-down laptop, a higher-capacity model of the iPhone and a digital movie-rental service, Mr. Craig wrote.