General Motors Corp. almost tripled its 1981 earnings to $963 million ($3.09 a share) last year despite an 8 percent plunge in car and truck sales to 6.2 million vehicles from already depressed 1981 levels, the No. 1 U.S. automaker said yesterday.

GM's 1982 earnings compared with profits of $333 million ($1.07) in 1981 on sales of 6.8 million vehicles worldwide.

Dollar sales for 1982 were $60 billion, down 4 percent from $62.8 billion in 1981.

In other major earnings reported yesterday:

* Sears, Roebuck & Co., the nation's largest retailer, said yesterday that its net income rose 38 percent in the fourth quarter and 33 percent for the year over 1981 levels as its Allstate Insurance Group and Sears Merchandise Group reported record income for the year.

* CBS Inc. said fourth-quarter profits fell 12 percent from a year earlier and full-year net income was off 31 percent on losses from discontinued operations.

GM earned $145 million in the fourth quarter (45 cents) compared with $97 million (31 cents) in the last three months of 1981.

GM Chairman Roger Smith and President F. James McDonald called 1981 "another year of mixed economic results."

The 1982 profits are the largest for GM since 1979, when the automaker earned $2.89 billion ($10.04). GM lost money for the first time in 1980.

Other automakers' earnings are due out in the next few weeks.

GM's good showing for 1982 was due largely to cost-cutting, use of income tax credits and big profits for the automaker's subsidiaries, said independent industry analyst Arvid Jouppi in Detroit.

Cost-cutting was evidenced by a drop in GM's worldwide work force from 741,000 in 1981 to 657,000 last year. Its payroll dropped to $17 billion from $19.2 billion.

GM had an operating profit of $961.9 million last year compared with $392.1 million in 1981. Sears, Roebuck & Co. reported record fourth-quarter net income of $459.4 million ($1.31 a share) compared with $333.1 million ($1.05) in the last three months of 1981. Revenue increased 10.4 percent to $8.9 billion from $8 billion.

Net income for the year was $861.2 million ($2.46) compared with $650.1 million ($2.06) in 1981. Revenue for the year increased 9.7 percent to $30.02 billion from $27.36 billion in 1981.

Sears' Chairman Edward R. Telling said all of the company's business groups reported improved results for the fourth quarter, and he attributed the success to reduced interest rates, better investment climate and continued tight expense controls. CBS Inc. said that its 1982 losses from discontinued operations mainly reflected the company's disposition of Pacific Stereo, its retail electronics chain, and CBS Cable, its pay-TV cable programming service.

In the fourth quarter, CBS said its income from continuing operations was $52.5 million. A loss of $16.8 million from discontinued operations made final net income $35.7 million ($1.27 a share). A year earlier, CBS posted net income of $40.5 million ($1.45) after a loss of $27.9 million from discontinued operations. Revenue rose 8 percent to $1.22 billion from $1.13 billion.

For the full year, CBS' income from continuing operations was $150 million, down 25 percent from $200.2 million in 1981.

In 1982, losses from discontinued operations of $37.5 million lowered final net income to $112.5 million ($4.01). In 1981, losses from discontinued operations were $37.4 million, lowering net income that year to $162.8 million ($5.83). Full-year revenue rose to $4.12 billion from $3.96 billion.

The company's broadcasting group posted higher revenues but lower profits, "reflecting both a lackluster sales environment and first-year costs associated with important investments in expanded news and sports programming for the television network and in a new radio network service," CBS said.

But CBS said its television stations division had a record year and that its TV network ended the year "in its strongest competitive position in six years."

The records group's revenues and earnings declined, while the publishing group had higher revenue but lower profits, CBS said.