The stock market rolled up its second strong gain in a row today, responding to declining interest rates.

Savings and loans, utilities and other issues sensitive to interest-rate developments posted some of the day's best gains. But the broad-based advance also showed up clearly in the oil, gambling and glamour stocks.

The Dow Jones average of 30 industirials climbed 12.38 points to 953.16 on top of Tuesday's 8.19-point gain.

The New York Stock Exchange composite index, up 1.43 points to 72.71, and the American Stock Exchange market value index, up 4.52 points at 333.14, both reached record highs.

Big Board volume accelerated to 52.37 million shares from 35.29 million the day before.

Analysts said the post-Labor Day rally in stock prices has been closely linked to a downturn in interest rates in the bond and short-term money markets.

Those rates had been rising in recent weeks, threatening to put new cost pressures on businesses that borrow heavily and attract money away from stocks into bonds.

"With rates coming back down again, it's a big plus for the stock market," said Hildegarde Zagorski, an analyst at Bache Halsey Stuart Shields Inc. s

Cash-laden institutions, on the side-line Tuesday, were active in this market, as the heavy volume and large number of block trades indicated. After a week-long pause, the spring-summer rally may have been reborn.

Among savings and loan issues, one of the most volatile interest-rate-sensitive groups, Fidelity Financial rose 1 1/4 to 14 as of the 4 p.m. close in New York; Imperial Corp. of America 2 1/2 to 31 1/4; and Golden West Financial 1 1/2 to 18 1/2.

Dow Jones' average of 15 utility issues, meanwhile, posted a 1.86-point gain to 113.36.

In the gambling sector, Caesars World picked up 1 3/8 to 17 3/8; Bally Manufacturing 1 1/2 to 28 5/8; Playboy Enterprises 1 1/8 to 16 7/8; Ramada Inns 1 1/8 to 10; and Resorts International class A stock 1 3/4 to 33 5/8 on the Amex.

Gainers among the oils included Exxon, up 1 1/8 at 71 7/8; Getty, up at 74; Conoco, up 1 at 53 5/8; and Texaco, 7/8 higher at 38 1/4.

Texas Instruments jumped 5 5/8 to 125; International Business Machines 1 3/8 to 67 1/2; and Xerox 2 3/8 to 61 1/2 among the glamors.

AMF gained 1 1/4 to 22 3/8 in active trading. The company said it knew of no reason for the stock's strength.

Documation lost 3/4 to 16 3/8. Storage Technology yesterday signed a letter of intent to buy Documation for about $52 million in stock. Storage Technology added 1/2 to 19 7/8.

Outlet Co. gained 1 1/8 to 31 after the company revealed it has information that several persons are interested in buying one or more of its retail stores. t

Dutch Boy Inc. advanced 3/4 to 14 3/4. The company sold its Solar Electric Corp. unit to North American Phillips Lighting Corp. for about $6 million.

The daily tally on the NYSE showed gainers outstripping losers by more than a 4-to-1 margin.

Standard & Poor's index of 400 industrials rose 2.12 points to 142.57, and S&P's 500-stock composite index added 1.92 points to 125.66.

In the over-the-counter market, the NASDAQ composite index closed at 184,53, up 2.19 points.