General Motors Corp.'s first-quarter profits tumbled 33 percent from a year earlier, and American Motors Corp. lost $51 million in the period--its eighth straight quarterly loss.

GM, the nation's leading automaker, said its earnings fell to $128.3 million (41 cents a share) from $190 million (63 cents) a year earlier as sales fell to $14.7 billion from $15.7 billion.

AMC had lost $52.7 million in the January-March period of 1981--its largest deficit for those three months. AMC's sales in the latest quarter edged up to $600.2 million from $598.4 million a year earlier.

GM Chairman Roger B. Smith and President F. James McDonald attributed GM's profit to continuing cost reductions and favorable foreign currency translation gains, which helped offset declining car sales.

Smith and McDonald said the sales drops, tied to the prolonged national recession, brought worldwide sales of vehicles to dealers down 13 percent, from 1.69 million in the first three months of 1981 to 1.47 million in the period this year.

GM earned $333 million for all of last year.

AMC, which lost $136.6 million in 1981, said its sales of cars and Jeeps to dealers worldwide totaled 56,400 in the first quarter, down 21 percent from 71,277 in the period in 1981.

AMC Chairman W. Paul Tippett said "industry retail sales were adversely affected by a stagnant economy, high interest rates and bad weather."

AMC and GM were the first U.S. automakers to report first-quarter results this year. Spokesmen for the other companies said their results would be released later this week.

Atlantic Richfield Co., the nation's seventh-largest oil company, and Union Oil Co. of California, ranked 15th, yesterday reported higher first-quarter profits.

In the latest quarter, Arco's earnings rose 5 percent to $385.4 million ($1.53 a share) from $368.4 million ($1.47) in the opening quarter last year. Revenues dropped 10 percent to $6.4 billion from $7.1 billion.

Arco Chairman Robert O. Anderson said stepped-up crude oil production from Alaska and higher petroleum product margins were key factors in the earnings' gain.

Union Oil's first-quarter earnings advanced 9 percent to $168.5 million (97 cents) from $154.5 million (89 cents) in the same 1981 period. Revenues fell 7 percent to $2.48 billion from $2.68 billion.

Union Chairman Fred Hartley said the stronger profits largely reflected improved refining and marketing operations and earnings from natural gas production in Thailand.

Procter & Gamble Co., a leading maker of soaps, detergents and other household and consumer products, said yesterday that profits for its fiscal third quarter rose 15 percent from a year earlier on a 5 percent gain in sales.

The company said its earnings in the quarter ended March 31 rose to $198 million ($2.39 a share) from $172 million ($2.09) a year earlier. Sales rose to $3.09 billion from $2.95 billion.

Nine-month profits rose 17 percent to $612 million ($7.40) from $524 million ($6.34) as sales climbed 5 percent to $9.02 billion from $8.62 billion.

Boeing Co. said yesterday that its first-quarter profits fell 58 percent from a year earlier on a 17 percent drop in sales.

The aircraft maker's earnings were $61 million (63 cents a share) compared with $144 million ($1.49). Sales declined to $2 billion from $2.42 billion.

Boeing said the earnings decline was attributable to significantly lower commercial jet transport deliveries, continued high research, development and engineering costs for the new 757, 767 and 737-300 jetliners, and lower interest income.

Rockwell International Corp. said yesterday that its sales and earnings increased slightly during its second fiscal quarter despite a "worldwide recession." Rockwell, a diversified company with automotive, aerospace, electronic and other businesses, reported earnings of $94.8 million ($1.24 a share) on sales of $1.83 billion for the quarter ended March 31.

A year earlier, the company earned $92.6 million ($1.22) on sales of $1.79 billion.

First-half earnings were $156.7 million ($2.05), an increase of 6 percent from $148 million ($1.95) a year earlier. Sales gained to $3.45 billion from $3.43 billion.