Courageous, the 10-year-old America's Cup sentimental favorite, emerged from a fog bank today as the startling early front-runner in final trials for the right to defend the cup.

After waiting an hour for thick haze to clear so racing could begin on Rhode Island Sound, Courageous defeated defending champion Dennis Conner's red 12-meter Liberty twice straight in moderate southerly winds.

It was a remarkable reversal of fortunes in the first meeting of these two in the final series of summer-long trials to pick a defender.

Liberty was odds-on favorite to win these trials, having finished July racing with nine straight victories over Courageous and the third U.S. contender, Defender. Meantime, Courageous was in a July funk, winning only twice all month.

But today, sporting new sails and minor adjustments to her hull, the sleek, white two-time cup champion from a decade ago managed not only to beat brand-new Liberty, but came back from deficits twice in the racing to reclaim lost leads.

Courageous skipper John Kolius, celebrating his fourth wedding anniversary while a hurricane advanced on his native Houston, steered his way to three-second leads over Liberty at both starts.

The 32-year-old skipper lost the lead early in the first race during a tacking duel, then regained it at the end of the first leg when a fortuitous wind shift lifted him 12 seconds ahead and left Conner briefly wallowing.

But Kolius fell back again on the next tack when a guy wire on the big spinnaker came flying loose as he raced along under full sail, the wire flailing wildly and leaving one crewman with a bloody lip. "That cost us about four boat lengths and the lead," said Kolius later, the breakdown taking two minutes to repair.

But Courageous retook the lead the next time the boats went upwind, scooting ahead on boat speed alone, and as the day wore on she proved consistently to be superior to Liberty when racing into the wind. It is a strong tack to be better on, since more than half of each America's Cup race is conducted dead into the breeze.

Kolius won the first race by five seconds as Liberty closed on a final downwind leg, but won the start again in the next trial and never relinquished the lead, triumphing by 10 seconds the second time.

Conner, to whom losing in August is something of a novelty after his shellacking of the opposition in 1980, said of the races, "They were very close. After 30 miles of racing, you can't get any closer than 15 seconds between boats."

Courageous' crew seemed near delirium at the close of the proceedings. They raised fists in triumph as their fans in the spectator fleet bleated boat horns in appreciation.

This was not the scenario envisioned by many fans. Courageous was thought to have finished her work, having pushed the two new American yachts to go faster by serving as a summer trial horse. Even her admirers expected Courageous would be given a chance to run a few races in these finals trials as a reward for her service, then dispatched by the selection committee. But Courageous led Defender around the course for most of Tuesday, opening day of the finals, and now she's vanquished favorite Liberty twice in a row.

It left some of Kolius' Houston admirers thinking great thoughts. "It sure puts a lot of pressure on the selection committee," said Texas lawyer Thad Hutcheson, a former Soling national champion and longtime friend of the Courageous skipper.

"They've put a lot of weight on Conner," he said, "and now they have to face the prospect of picking a guy who never raced a 12-meter. But the fact is, to race a crowd like the Australians, you need a guy who will stand up and punch you in the nose. That's Kolius."

Australia II continued her mastery of the foreign fleet today, beating Azzurra by 2 minutes 26 seconds. That puts her record at 5-0 in the nine-race challengers' semifinal trials and assures her a spot in the finals. Britain's Victory '83 won over Canada to up her second-place record to 4-1, but the Canadians protested a starting maneuver so the victory was not immediately official.