In the early morning light, the hunter stalked an antelope over a small knoll on the high desert plains. Twice, he raised his rifle, but didn't shoot; the third time, he squeezed off a round. The buck, 350 yards away, bolted and ran 50 yards before falling, dead.

"When he started moving to the left, I wanted him to drop," joked Interior Secretary James G. Watt, whom Shoshone Indians here have named Eejjopo (pronounced Ee-zha-po), meaning "coyote" or "sly one." Watt downed his antelope Saturday in the Lander One-Shot Antelope Hunt, an annual event opening the season in western Wyoming.

Watt had risen at 4 a.m., breakfasted, and set out in darkness with two guides, a competing hunter and Tom Graham, part-owner of a 6,000-acre spread in this hilly sagebrush country. For the controversial Watt, it was a chance to modify his image as a desk-bound, development advocate who only visits the wild lands he manages in a big van or on a dirt bike.

It was also a day of driving and stalking, of eating and music and joshing. "It's good to be with real people," Watt said.

In the one-shot hunt, begun in 1939, teams of three hunters, often celebrities or politicians, challenge Wyoming's governor and his team to see which trio can bring down three antelope in the shortest time. Each hunter officially gets one shot -- a limitation designed to recreate conditions similar to the days when frontiersmen used one-shot muzzle loaders.

Watt's antelope didn't count in the competition, however. He had already used up his one official shot an hour earlier -- and missed. A team of outdoor writers won.

Wildlife advocates in Wyoming do not object to the hunt; antelopes are not scarce and those just wounded are quickly dispatched. Yet Watt's party expected controversy. "I don't know whether to hope that Jim hits or misses," said Bureau of Reclamation chief Robert Broadbent, who was on Watt's team. "But if he hits, they'll crucify him."

In Washington, Lewis Regenstein, vice president of the Fund for Animals, a wildlife protection group, said that while antelope is not an endangered species, "We don't think there's anything particularly sporting or virtuous about the nation's chief protector of wildlife gunning down a defenseless antelope."

But among the hunters here, Watt was a hit. Said Carroll Hutchens, an Oklahoma dentist, "You can sit down and talk to him for a few minutes and feel like you've known him all your life. He's not afraid of the heat."

Watt's department manages much of the land where the antelope roam, and its new grazing regulations affect ranchers like Tom Graham. Just north of Watt's hunting site, the ranchers complain that wild horses are destroying the range; Watt says federal laws protect the horses.

The state also is embroiled in debate over its Republican congressional delegation's wilderness bill, which goes far beyond Watt's proposals to protect wilderness areas from oil and gas development. The Sinks Canyon ski area, where hunters sighted their rifles on Friday, is one of several public land tracts being considered for possible sale under the Reagan administration's "privatization program."

And there is the Wind River Indian Reservation, where Watt on Thursday attacked Interior's own Bureau of Indian Affairs for its failures.

But at the hunt, all was jovial. Shoshone leader Darwin St. Clair would not say why the Indians dubbed Watt "Coyote," but said, "Everything is friendly here."

"This is not business, it's pleasure," said Wyoming's easygoing governor, Ed Herschler, a Democrat who has had some run-ins with Watt's department.

Watt's team was under some pressure to measure up to federal teams of the past, including one led by predecessor Cecil D. Andrus. During practice at the shooting range, Watt looked sharp, but said he hadn't hunted in 20 years. His press aide, Doug Baldwin, said the secretary, who had never hunted antelope before, borrowed a custom-made .25-06 rifle.

Watt missed his first buck, from about 200 yards; an hour later he fired a second shot and made a clean kill.

Later, when the governor asked, with mock gravity, "Jim, what happened?" Eeejjopo smiled and shrugged. "I just took one practice shot," he said, "and then I shot one."