Trading on the New York Stock Exchange, driven by aggressive institutional investors, reached a record 146.07 million shares today, sharply boosting blue-chip stocks amid widespread expectations of falling interest rates.

The Dow Jones Industrial Average rose 21.71 points to 965.97, a two-day gain of about 59 points. It was the highest close for the Dow industrials since July 1, 1981.

The bond market was also very strong today, as 20 new issues were able to bring a total financing package of about $2 billion, activity that Thomas Saunders, managing director at Morgan Stanley & Co., called "extraordinary."

"It is an institutional stampede," said Lou Smith, a technical analyst with Bear, Stearns & Co. "People are buying just for the sake of buying and milking stocks to the fullest. No one wants to miss the stampede."

The Wall Street rush was aided by the news that several major banks cut their prime rates from 13 1/2 percent to 13 percent today, and Chemical Bank, the nation's seventh largest, cut the rates for most consumer loans by a point and a half.

There is also a growing consensus among market specialists that the Federal Reserve has decided to loosen controls on the money supply and as a result is bringing down interest rates. Saunders noted that short bond rates are at a two-year low.

"What started yesterday has really exploded," said Eldon Grimm, an analyst at the brokerage firm of Birr, Wilson & Co. "We have this theory that the Federal Reserve is going to let the money supply grow faster. That sparked a rally in the bond market and spilled over into the stock market."

Charles Comer of Bache Halsey Stuart Shields said a number of his firm's major clients who had been reluctant to enter the stock market "finally said we can't afford to miss the move." So, he added, "They are throwing money at the same old big names.

"They are aggressively buying and saying the hell with the price," Comer said. "Right now you don't want to get in the way of the herd."

Clearly fueling the current stock and bond market boom are extraordinary amounts of cash and cash equivalents in the hands of large financial institutions and pension funds.

Furthermore, investors are also bringing to the markets money tied up in All Savers accounts, which come due this month, and in money fund accounts, which are being depleted as rates fall. "There is tremendous and continuing buying power in the market," Saunders said.

On the New York exchange, the trading volume easily topped the record of 137.33 million shares set Aug. 26, and was sharply higher than yesterday's volume of 93.5 million shares. The big gain in Dow industrials was also matched by a sharp jump in the Dow transportation average, which rose 9.59 points, closing at 382.87.

Advancing stocks outpaced declining issues by more than four to one, as 1,372 stocks gained in per-share price. The New York composite index was up 1.57 points, and the average price per share there rose by 65 cents.

The market was led by American Telephone & Telegraph Co., which jumped a point to 59 1/2. International Business Machines Corp. rose by 1 3/8 to 80 3/8 and Warner Communications Inc. jumped 1 7/8 to 45.

Johnson & Johnson, whose subsidiary makes Extra-Strength Tylenol, was the third-most-heavily-traded stock. It fell 1 3/8 to 40 3/8. Seven people have died from cyanide-contaminated Tylenol capsules.

Meanwhile, the American Stock Exchange market value index jumped 6.19 points to 294.47, as volume rose sharply to 9.3 million shares, up from 6 million shares yesterday. The average share price on the Amex rose by 25 cents, as 449 stocks rose and 184 declined.

Nationwide turnover in NYSE-listed issues, including trades in those stocks on regional exchanges and in the over-the-counter market, totaled 168.016 million Standard & Poor's index of 400 industrials rose 3.14 to 143.82, and S&P's 500-stock composite index was up 2.83 to 128.80.

On the over-the-counter market, 1,168 NASDAQ stocks rose and 234 declined. The NASDAQ composite index was up 3.61 points, closing at 195.59, and NASDAQ's industrial index jumped 4.30 points to 222.42.