The Supreme Court yesterday let stand an award of $7,851,493 in actual and punitive antitrust damages against Greyhound Corp., giving a major victory to a resolute small competitor who had been marked for destruction by the Nation's largest operator of inter-city buses.

But the jutices agreed to review a lower court's ruling that awarded Mr. Hood Stages of Bend, Ore., an additional $5,294,597.

The Ninth U.S. Circuit Court of Appeals ruled that Greyhound owned the $5.3 million fora period after 1968, rejecting a company argument that the Sherman Act no longer applied.

The Greyhound claim - which the Supreme Court will review - is that the four-year statue of limitations in the law began to run on Dec. 14, 1964, when the Justice Department intervened in an Interstate Commerce Commission proceeding against Greyhound.

The total award won by Mr. Hood was $13,146,090, not counting about $6 million in interest, attorneys' fees and court costs. The 20-year period involved ended when trial of Mt. Hood's suit began in 1973.

On 10 separate occasions during 14 years of litigation, the Ninth and Seventh circuit courts of appeal, federal judges in Illinois and Oregon and the ICC condemned Greyhound's conduct as predatory, collusive, frudulent and willfully contemptuous of court and agency orders.

In 1971, acting on ICC and Juctice Department motions, a federal judge in Chicago held Greyhound in criminal and civil contempt and fined it $600,000.

Mt. Hood, owned by William J. Niskanen, operates in Oregon, Idaho and Utah.

Between 1947 and 1956, Greyhound bought out eight bus lines in Mr. Hood's operating region. Four of the lines encircled Mr. Hood, allowing Greyhound to route traffic around his territory, Niskanen contended before the ICC.

Greyhound promised the ICC that it would continue to honor an agreement with Mt. Wood under which, Greyhound by using the small firm's lines for parts of certain trips, passengers could save up to 110 miles and more than four hours' travel time. Passengers, unaware that a less cirucuitous routing was available, paid up to $40 extra for the detours.

Accepting Greyhound's assurances, the ICC approved the acquisitions. Later, however, the agency found that Greyhound had dishonored its commitments and had tried to ruin Mt. Hood as a substantial competitor with "destructive competition."