After flirting with bull-market history for several days, the widely followed Dow Jones industrial average convincingly punched through the 1,500 level yesterday, adding 12.5 points to close at an all-time high of 1,511.7.

"All signals were go," declared Hildegarde M. Zagorski, market strategist at Prudential-Bache, noting that the strength of the rally was confirmed by several broader market averages. It took only 25 trading days for the rapidly moving Dow to rise from 1,400 to 1,500.

The new top was reached on a volume of 178 million shares, the fifth-heaviest day on record at the New York Stock Exchange, where 25 billion shares have changed hands so far this year. Total sales are 2 billion shares ahead of 1984.

According to Wall Street strategists, the market's steady run has been propelled by sliding interest rates, hopes for action on the federal budget deficit, a climate of low inflation helped by expectations of lower oil prices, international action against the dollar's strength relative to foreign currencies, signs of an economic pickup and institutional investors hoping to improve end-of-year performance.

John D. Connolly, chairman of the investment policy committee at Dean Witter, yesterday emphasized the role played by legislation designed to shrink the federal budget deficit and arrive at a balanced budget by 1991. "That's been in control of the market for the past six or seven weeks," he said. "It's been joined by the oil price situation . . . and both are pushing expectations of inflation down."

Connolly said he expects to see the Dow industrials reach between 1,750 and 1,800 in 1986.

Robert Farrell, chief market strategist for Merrill Lynch, enjoyed yesterday's landmark performance by the Dow industrials. During a speech in Washington last spring, Farrell predicted the Dow would reach 1,500 by the end of this year.

Farrell said he still is surprised at how strong the rally has been. He also said he expects the Dow Jones industrials to top 1,600 in the first half of next year, then to settle down for a "long consolidation" period. He said that he also expects to see a market correction of between 5 and 10 percent during January.

Part of an influx of institutional money into the market was because of the failure of 70 percent of the professional money managers to beat the market averages, Farrell said. As a result, they are leaping into various stocks and switching stocks to try to improve their performance.

The bond market, meanwhile, rallied as interest rates dropped. Prices of long-term government bonds, which move in the opposite direction from interest rates, rose $10 to $15 for every $1,000 in face value.

The market's gains came in spite of a legal setback for Texaco when a Houston judge upheld a jury decision ordering Texaco to pay Pennzoil Co. more than $10.5 billion plus interest for wresting control of Getty Oil from Pennzoil. Texaco, a component of the Dow Jones industrial average, fell 2 1/2 to 28 1/4 on volume of more than 8.4 million shares. Pennzoil shares climbed 2 5/8 to 68 7/8.