No venue showcases Serena Williams’s dominance of women’s tennis like the All England club. And no opponent elicits her best like Maria Sharapova, who was just 17 when she dethroned Williams in the 2004 Wimbledon final.

Williams has been paying back the Russian since. And she did so again Saturday to claim the lone coveted prize to elude the 30-year-old champion: Olympic singles gold.

It was an unapologetic evisceration, with Williams needing just 63 minutes for the 6-0, 6-1 victory.

And she leaped up and down on Centre Court, where she won the fifth of her Wimbledon championships four weeks earlier, then erupted into a celebratory dance as her sister Venus snapped photos from a courtside box.

With the victory, Williams became only the second woman and fourth tennis player in history to accomplish what’s known as the “Golden Slam,” winning all four of the sport’s majors and Olympic singles gold. Andre Agassi, Steffi Graf and Rafael Nadal did so, as well.

“I never played better,” Williams told reporters afterward. “I have my gold medal [in singles], and now I have everything, literally. I have singles, doubles — actually everything there is to win in tennis. Where do I go from here?”

Serena Williams wasn’t the only American celebrating on Centre Court on Saturday. Twins Bob and Mike Bryan, who have claimed nearly every title of significance in the sport, exulted after finally winning Olympic gold in men’s doubles.

“We have always dreamed about standing on the podium, seeing the flag go up,” Mike Bryan said. “We could end tomorrow, and we’re going to be happy for the rest of our lives.”

Added Bob Bryan: “There’s no bigger match we’d rather win than that one: Centre Court, Wimbledon, for our country, for each other. We’re 34 years old, and we’ve played tennis since 2 years old. That’s a lot of balls going across the net, and this is it! This is the top of the mountain.”

That’s how Williams felt, as well, adding one more achievement to a résumé that is staggering, particularly given the injuries and illness she has battled throughout a 16-year pro career.

Williams has won 14 major titles, the most of any active player in women’s tennis and sixth all-time. She also has 13 Grand Slam doubles titles, all shared with Venus. And she has three Olympic gold medals, with the possibility of a adding a fourth Sunday.

Just three hours after Serena won singles gold, she returned to the same, well-trodden Centre Court with Venus to defeat a sturdier pair of Russians, Nadia Petrova and Maria Kirilenko, 7-5, 6-4, to earn a place in Sunday’s women’s doubles final.

They’ll face the Czech tandem of Andrea Hlavackova and Lucie Hradecka for what would be their third Olympic gold in doubles, having triumphed at the 2000 Sydney Games and in Beijing in 2008.

In a way, Serena’s ruthless display of force and skill against Sharapova was a measure of respect for the Russian, whom she has utterly dominated since losing the 2004 WTA Championship final. Since that defeat, Serena is 8-0 against Sharapova and hasn’t allowed the Russian to win even a single set against her in four years.

But Williams knows well that Sharapova is the only player in women’s tennis with a competitive fire as fierce as hers. And before Sharapova could summon a rally of consequence, Williams quashed it.

“Playing against someone like Maria, you have to be at your best,” Williams said. “I know that, so it was like I had nothing to lose. . . . Against Maria, if you give her any hope, she’s trying to come back. She’s so good at that.”

Williams blasted three aces in the opening game and raced to a 2-0 lead without allowing Sharapova a single point.

While no woman likely could have denied Williams gold Sunday, it was clear that Sharapova had even less chance amid the gusting winds.

Williams, who boasts the best serve in women’s tennis, smartly lowers her ball-toss when competing in such aggravating conditions. And she can do so without compromising her serve’s power or placement.

At 6 feet 2, Sharapova can lower her aberrantly high toss only so much. And because her serve is a liability to start with, it got ugly fast. With her serve betraying her, Sharapova seemed to break down in every facet of her game. Her footwork was leaden. And her best groundstrokes were whimpers compared to Williams’s thunderclaps.

Midway through the second set, a BBC commentator declared that the proceedings “resembled more blood sport than tennis.”

It was true.

Sharapova’s only opening was minuscule and fleeting, coming in the fifth game, in which she finally got a break point on Williams’s serve, and then another.

Williams crushed both.

The Russian committed a rash of double faults to hand Williams a 5-1, second-set lead. And Williams blasted back-to-back aces to bring the match to a merciful conclusion.

“She has got such great form,” Sharapova said of Williams. “She was just too stubborn, too strong for me today.”

Williams defeated four former world No. 1 players en route to the 2012 Olympic gold medal: Jelena Jankovic, Caroline Wozniacki, Victoria Azarenka and Sharapova.

Asked to explain her dominance over Sharapova, who also was seeking a Golden Slam and would have reclaimed the No. 1 world ranking with a victory Saturday, Williams said: “I think I was just focused. I don’t think she did anything wrong. I was blind today. It was just something about today and this tournament.”

The women’s singles bronze medal went to Belarus’s Azarenka, who’ll retain her No. 1 ranking following her 6-3, 6-4 victory over Kirilenko.

On Sunday, Switzerland’s Roger Federer seeks a Golden Slam as well when he takes on overwhelming home-court favorite Andy Murray in a reprise of their riveting July 8 Wimbledon final.