Marriott Corporation made more money on all its major businesses last year and total profits jumped 31 percent to a record $71 million ($1.9 a share) from $54.3 million ($1.43), the Bethesda food, lodging and leisure company reported yesterday.

Marriott's sales for the calendar year increased 21 percent to just over $1.5 billion from $1.25 billion.

For the final quarter of 1979, Marriott's earnings were up 23 percent to $17.3 million (51 cents) from $14.1 million (37 cents); sales for the period gained 19 percent to $457 million from $383 million.

"All five of our businesses reported gains for 1979," said President J. W. Marriott Jr. in a statement released with the earnings report. "Emphasis on labor productivity and cost controls helped expand our profit margin," he said.

The biggest percentage gains were turned in by Marriott's pair of theme parks, which have made little money in the past. Theme park profits were up 48 percent and attendance matched the previous year's levels despite gasoline shortages and a shorter operating season.

Gasoline shortages hurt the fast food busines, Marriott said, and earnings were off at the Big Boy and Roy Rogers chains. But total profits of the restaurant division increased 4 percent as a result of gains by the Farrell's and Hot Shoppes operations.

Marriott's Hotels reported a 31 percent increase in sales and a 30 percent gain in profits, and occupancy rates were up to "well above the 80 percent level."

The contract food service division turned in a 34 percent boost in earnings on a 24 percent increase in sales. Record airline travel increased earnings of the company's inflight and terminal services, but Marriott restaurants at major Highway rest areas reported lower earnings.

The company said its cruise ship division, Sun Line, also improved its earnings, but gave no specifics.