For a decade, Texas has been one of America's economic success stories, but a new reality set in here today when the Labor Department announced that the unemployment rate had jumped 1.7 percentage points in the single month of September.

While still below the national figure of 10.1 percent, the Texas unemployment rate of 8.4 percent stands at its highest level since the state began keeping monthly figures in 1970.

"It's a rather remarkable increase," said Terence Travland of the Texas Employment Commission. "We haven't had a chance to study the numbers, but our first impression is that the recession . . . is getting a firm grip on the Texas economy."

With the release of the figures today, unemployment is likely to become the central issue of debate in the heated gubernatorial campaign between Republican Gov. Bill Clements and Democratic Attorney General Mark A. White.

A year ago, Texas seemed immune to the economic slump setting in elsewhere, but from oil to agriculture to manufacturing, from the Panhandle to east Texas to the Mexican border, virtually the entire Texas economy is suffering.

"This is the worst recession we've had since 1970, and maybe even worse than that," said Bill Gruben, the Dallas Federal Reserve Bank's expert on the Texas economy.

Up to now, the state's expanding economy was able to absorb new workers from other parts of the country without a marked increase in unemployment.

But some economists believe those days are in the past. In August, for the first time in a decade, total nonagricultural wage and salary employment in Texas fell below the levels of the same month in the previous year.

From now on, some economists expect the Texas economy to perform more like the national one. Gruben even argues that the recession may linger longer in Texas than in other states, although other economists disagree.

Oil kept Texas booming while other states were beginning to slump. But, beginning last spring, the bottom fell of the industry that permeates the state's economy. The Hughes Tool Co.'s rotary rig count, a barometer of the Texas economy, has fallen 46 percent nationally since the end of 1981, and Texas has taken a direct hit.

But the economic woes of Texas are not limited to oil:

* Despite increased defense spending, the electronics and electrical equipment industries have been slumping since late 1980. Texas Instruments of Dallas has laid off 7,000 workers worldwide since the spring of 1981, 4,000 of them in Texas.

* Low prices and bad weather have hit farmers in the Panhandle, and agricultural experts predict that cotton production will be at its lowest level since 1946. Thousands of farmers are delinquent in their loans.

* The slump in home building has hurt the timber industry in east Texas, while the fading of "Texas Chic" has cut production in the apparel industry.

* The devaluation of the peso has intensified the recession along the Mexican border. Retail sales in some cities are estimated off by up to 40 percent, and the real estate industry is feeling the pinch.

Up to now, many Texans, including Clements, have treated the gathering recession with a combination of optimism, bravado and disbelief.

Last summer, Lone Star Steel Co. in Lone Star announced that it would lay off more than 3,000 workers. In September, the Rotary Club in nearby Greenville took up a collection to help unemployed steelworkers. The club gathered $1,100--and promptly sent it to Midland, Pa.

The mayor of Lone Star cried foul, arguing that the money should have stayed at home, but Clide Wilcox, president of the Greenville Rotary Club, disagreed.

"The people in Pennsylvania had already used up their unemployment insurance," Wilcox said. "The people in Texas had not. I've said that when the people in Texas use up their benefits, then our club would help them."