LONDON — Three down, just one to go.

In her long and ever more remarkable career, Serena Williams has won all the major tournaments at least three times. She has won Olympic gold in singles and doubles. She has won WTA Tour events large and small.

But what she has not yet managed is a Grand Slam: winning the Australian Open, the French Open, Wimbledon and the U.S. Open in the same calendar year.

Williams’ 6-4, 6-4 victory over Garbine Muguruza of Spain in the final Saturday gave Williams her sixth Wimbledon singles title and her fourth straight major singles title — the so-called Serena Slam. But it also gave her the first three legs of the Grand Slam, the true Slam, which could make this year’s U.S. Open quite an occasion.

Despite the straightforward score line, the opportunity did not come easily. Muguruza, 21, playing in her first Grand Slam final, displayed few signs of nerves and plenty of purpose in the opening phase of the match and took a 4-2 lead before Williams turned the momentum in her favor.

Williams double faulted three times in the opening game and lost her rhythm again while serving for the title at 5-1 in the second set. With the Centre Court crowd giving Muguruza plenty of positive reinforcement, she surprisingly broke Williams’ serve twice in a row, saving a match point and getting back on serve to 5-4.

But the rally (and the rallies) would end there as Muguruza lost her serve at love, missing a forehand wide on Williams’ second match point.

It was unclear initially whether Muguruza would challenge the call, but the ball was clearly out. No challenge came, and the chair umpire Alison Hughes haltingly pronounced the words: “Game, set and match, Miss Williams.”

Williams, delayed reaction or not, was soon leaping on the grass and celebrating. Muguruza was in tears sitting on her chair.

“Don’t be sad,” Williams told her at the trophy ceremony. “You’ll be holding this trophy very, very soon. Believe me.”

Only three women have completed the Grand Slam: Maureen Connolly in 1953, Margaret Court in 1970 and Steffi Graf in 1988.

“It’s probably the only thing she hasn’t done yet,” said Patrick Mouratoglou, Williams’ coach.

In truth, there is also plenty of other history to chase, even as Williams’ contemporaries continue to work (and play) in her shadow.

This latest triumph broke the family tie with her older sister Venus, who has won five times at the All England Club and watched from the players box Saturday. This was also Serena’s 21st Grand Slam singles title, putting her just one behind Graf, whose 22 are the best of the Open era, and just three behind Court, an attacking Australian who won 24.

Serena won her first in 1999 at the U.S. Open, fighting her way through a draw of her elders to create quite a surprise.

To win her sixth Wimbledon, Williams had to beat three former No. 1 players on her way to the final: Venus in the fourth round, Victoria Azarenka in a tight quarterfinal and Maria Sharapova in the semifinals.

“She was kind of like an inspiration for me, because when I was watching the TV, I see her play finals, and she was No. 1,” Muguruza said last week.

On Saturday, Muguruza was the one across the net from Williams in a Grand Slam final; the one being watched on television in Spain and elsewhere around the globe.

But one thing has not changed, even after all these years. Williams is still No. 1.

Now, about that Grand Slam.