Tom Watson awoke early this morning, then went back to sleep and began dreaming. He dreamed about golf, about the British Open championship.

"One dream I had," he recalled, "I had to play golf through a corridor, through three rooms.

"No, I didn't dream I had won."

Victory may not have been in his dreams but Watson, who went into the final round of the 109th British Open golf championship leading by four shots, shot a sometimes-spectacular 69 to take the same margin to his third coronation in this oldest and most prestigious national golf championship.

Watson's two-under-par final round, added to earlier trips of 68, 70, and 64 over the 6,926-yard, par-71 links course, gave him a total of 271, second-lowest British Open score in history. It stands behind the 268 he shot to win at Turnberry in 1977. Watson also won in a playoff, 71-72, with Jack Newton after shooting 279 for four rounds at Carnoustie in 1975.

Second place was taken by Lee Trevino, the first-day coleader with Watson and second-day leader by three shots, who tallied 275 for his four rounds. Ben Crenshaw was next at 277 and fourth-place was shared by U.S. Open champion Jack Nicklaus and Carl Mason, the low Briton on the scoreboard, at 280. Coincidentally, the low five scorers all had 69 today.

Two shots further back at 282 were Craig Stadler (71), Andy Bean (72), Hubert Green (72) and Scot Kenny Brown (76). Pennsylvanian Jay Sigel was low amateur at 291.

Watson said he "didn't feel comfortable until I hit the ball on the 16th green. Then I knew I had it won."

He had it won long before that.

A run of five birdies in seven holes Saturday had bolted him into the lead and a run of five birdies in six holes today, marred by a bogey on the 10th hole, put it away, along with the first prize of 25,000 British pounds ($59,250 U.S. currency).

Watson had bogeyed the third hole when his second shot landed on a hillock left of the green, he chipped to eight feet and missed. Only Crenshaw, who started the day six shots back, had managed to pick up ground, by birdieing the tough opening hole with a 15-foot putt.

So when Watson sank a curling 18-footer on the 185-yard seventh hole to get back to 11 under par, his lead was four shots again, despite birdies at eight and nine by Trevino, offsetting earlier bogeys.

Watson then birdied the 444-yard eighth with a five-iron approach to seven feet and the 30-year-old freckle-faced redhead lit up a huge grin after he dropped a three-footer for birdie on the relatively easy 495-yard, par-5 ninth.

After a missed green and terrible chip cost him a bogey on the 10th hole, Watson picked up the birdie habit again. He drove only about 215 yards into a strong wind over the hill of the blind 386-yard 11th hole, then hit "the best golf shot I hit all week."

It was a five-iron dead against the strong wind that rolled four feet past the pin for an easy 3. Then he dumbfounded his playing partner, Brown, on the next hole. Watson used a three-iron off the tee on the 386-yard hole. He was fully 100 yards behind the colossal drive of Brown. However, Watson made his 15-footer after a nine-iron approach while Brown, who had pitched to 10 feet, missed.

It was the last of the Watson birdies, and he followed with a bogey on his opponents were concerned.

Brown's game was disintegrating at this point, and Trevino and Crenshaw, playing in the twosome ahead, but more than three holes in front, were running out of holes in which to make a charge.

Trevino was hopeful at one point over the huge hole gap between the twosomes, caused mainly by the fastidious play of Brown, a 23-year-old 6-footer who is so thin that if he closes one eye he can pass as a needle.

Trevino said at the turn, "I told Ben that if I could shoot a 32 on the back side, making me 10 under, it might make a difference. Watson was playing so far behind he would have to look at the score and it might make a difference in his game.

Trevino wasn't far off his mark, getting 33 on the incoming nine, but Watson, who said he was unaware of the others' scores from eight through 13, wasn't cooperating.

"I don't think I was ever less than three ahead and that's a fine cushion," Watson said at the awards ceremony. "Today, after No. 5, I knew I had the rhythm going."

Trevino, also a two-time winner going into this tournament, had won the last time it was played at Muirfield in 1972. He expressed no disappointment, however.

"It's no disappointment to finish second to the greatest player in the world," he said. "When you finish second to the greatest player in the world it makes you look like the second best."

Watson, who has won one Masters tournament in addition to the three British Opens (placing him with Nicklaus and Bobby Jones as Americans with three titles; Walter Hagen won four), was not about to make the claim of greatest player in the world, despite his record of 16 tournament victories the last three years, including six this year. "If you go by the record book, Jack Nicklaus is the greatest golfer who ever played the game," he said.

Nicklaus is hardly challenged in that respect and his adoring Scot fans appreciated the fine 69 he recorded today, including a birdie on the finishing hole, at a time when he had no chance of winning.

Conversely, defending champion Seve Ballesteros shot 74 for a 286 finish with a sloppy, what-does-it-matter round.

Crenshaw, another player well liked in Britain, dating back to a time he played in the Carroll's Irish Open and made a hit with Europeans with his pleasant manner, now has two seconds and a third in British Open play. "I'm just going to have to keep trying," the young Texan said.

"It was the best I've driven the ball in a major tournament," he said. "But I never could quite gauge my irons correctly."

Crenshaw had some explanation for the scores, especially in the middle rounds, that tore apart this venerable Links Course, the favorite in the British Isles of Nicklaus and Watson, among others.

"We had a little rain (to soften the greens)," he said. "There was no wind yesterday (Saturday), the pins were accessible, and the condition of the golf course (was superb). Also, when somebody sees a (low) score go on the board, it's like a domino effect."

Brown, whose putter had helped him to 68s in the second and third rounds, lost his touch today. He was disappointed to finish so poorly. "I was especially pleased with the support of the crowd."

That pro-Brown gallery caused one discomfort for Watson, who was greeted by a cheer when he missed one putt.

But nothing could take away the joy of victory. "Winning in Scotland is unlike winning anywhere else," he said. "The tradition . . . is unlike anything in the United States."

That tradition will continue in 1981 when the Open returns to Royal St. George's in Sandwich, England, for the first time in 32 years.