NEW YORK, OCT. 7 -- Shaking off a case of nerves caused by Tuesday's huge plunge, the stock market today staged a late rally to finish mixed in active trading.

The Dow Jones industrial average gained 2.45 points to close at 2551.08, but most other market indexes were unable to overcome early losses and finished lower for the day.

Analysts said that the half-point increase in the prime interest rate announced today had little impact on the market because most investors anticipated the action in trading Tuesday, when the Dow plummetted a record 91.55 points amid worries about renewed inflation and rising interest rates.

The prime rate increase also was shrugged off by the bond market, which showed early strength and closed a little lower. The Treasury's bellwether 30-year issue was down three-sixteenths point, nudging the yield up from 9.78 to 9.79 percent.

The stock market opened skittishly and then bounced sharply up and down during the early afternoon. At one point, the Dow average was off more than 30 points, but blue-chip stocks led a recovery during the last hour that pulled all the indexes back toward their starting points.

"I think people took encouragement from the fact that we didn't slide all the way into oblivion by early afternoon," said Ralph Acampora, a market analyst at Kidder, Peabody & Co. "There wasn't a black hole. {Tuesday} did some damage, but not to the extent that some people will have you believe."

Other analysts said that computerized stock trading programs, which contributed to Tuesday's sharp decline, helped bolster stock prices today. They said the programs sometimes exaggerate the market's performance during its closing hour, making it less likely that an upward or downward trend will carry into a second day.

Large, computerized stock trades "happen late in the day and they happen for nontraditional market reasons," said Justin Mamis, an analyst at Cowen & Co. "Nine times out of ten now, the market will close well one day and not open well the next day and vice versa."

Investors also were buoyed by the performance of the bond market, analysts said. Overnight indications about today's bond market performance were positive, reassuring investors that Tuesday's stock selloff did not necessarily augur a financial disaster.

"The firmness in the bond market encouraged some bargain-hunting" in stocks, Mamis said. "The under-the-breath muttering was that it can't be too bad because the bonds are strong."

Strong bond prices indicate that fears about rising interest rates may be cooling. That, in turn, may have encouraged investors today to stick with stocks, which have been soaring to record highs at irregular intervals since the first of the year.

Analysts said that investors will be watching closely over the next few weeks to see whether interest rates will rise further before the end of the year. They also will be keeping a sharp eye on third-quarter corporate earnings reports, which are due out soon.

The stock market's strong but volatile upward run during 1987, which has surprised a legion of doomsayers, has been fueled mainly by rising corporate earnings, analysts said. Continued earnings strength over the next few weeks will be important to investor confidence, they said.

"Earnings reports are going to be good," predicted Anne E. Gregory of Merrill Lynch & Co. Inc. "That should provide some support for the market."

Market bears, however, continue to insist that stock prices have far outstripped the underlying earning power of the country's leading corporations. "Longer term, I don't like the market. I think it's overpriced generally," said Rich Fontaine, a portfolio manager at Baltimore-based T. Rowe Price.