The first Australian Open quarter-final started at brunch for Melburnians, supper time for Americans, but in the end Venus Williams had Anastasia Pavlyuchenkova for lunch on Rod Laver Arena. The 36-year-old veteran wound back the clock to beat world No27 Anastasia Pavlyuchenko in straight sets, 6-4, 7-6 (7-3), and set up a semi-final appearance so unlikely that if she wins it and the outing after that, they should honestly make her a bigger trophy.

Immediately standing in her way is Coco Vandeweghe, who later beat Spain’s Garbine Muguruza 6-4, 6-0 to book a date with Williams in what will be an all-American last-four encounter.

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Tuesday’s opening match-up was no cinch. Over the past week Pavlyuchenkova had already made short work of higher-ranked seeds than Williams in the form of Elina Svitolina and Svetlana Kuznetsova, but the American knew her adversary had also never progressed beyond this point in a grand slam in 10 years on the tour, whereas Williams is a dab hand at grand slam finals in this her third decade of them.

Such nous told in this encounter. At 4-4 in the first set both players had been serving as poorly as the other, giving away a pair of breaks each, but it was Williams who held her nerve when it mattered, taking the first set 6-4 in 39 minutes. By then she had hit 13 winners to five, advancing to the net with relish.

Very little of the remarkable tension and sense of struggle could be read from the polite murmurs in the stands. Another by-product of becoming part of the furniture is that Williams no longer fills stadiums, but those who’d arrived punctually for the early start were well and truly in her corner. This is a career of two halves. In the last nine years Williams has reached only one grand slam final (2009 at Wimbledon) in 29 attempts. In the nine years prior she claimed seven titles and featured in five other finals.

In the third game of the second set Pavlyuchenkova broke, but got a little cute in her own following service game and lost it when Williams whipped a quite glorious double-handed backhand winner across court.

At 3-3 and 0-30 on serve, the American looked vulnerable, stomping both feet in quick succession to remind herself to move, but with a succession of forehand errors conceded the break which should have handed Pavlyuchenkova the set. The problem was that the Russian then played the reputation instead of the ball, so Williams broke straight back.

All of a sudden net rolls went the veteran’s way, and even straining as she looked into the sun, she held with ease to make it 5-4 and pile unbearable pressure on the Russian’s shaky serve.

Somehow Pavlyuchenkova survived to keep it on terms, so Williams produced a love service game so emphatic she may as well have walked over and packed Pavlyuchenkova’s bag for her at the change of ends. Utterly possessed from there, Williams hammered an vintage backhand winner down the line and its resonance surely played a role in the Pavlyuchenkova double fault that followed.

At 0-30, up 6-5, Williams needed to bury the content but couldn’t, and also didn’t seem thrilled by the prospect of the tiebreak that followed – a fear that proved well founded when Pavlyuchenkova raced out of the blocks for a 3-1 lead.

Nerves jangled, line calls were challenged, but Venus could not be denied, taking the match in an hour and 47 minutes of admirable if not always joyous tennis. While her jerking, limb-flailing style has never been pretty, everything Williams has done in Melbourne so far this fortnight has been timelessness and grace personified.

The whole crazy scene was best summed up as Williams levelled the tiebreak at 3-3 and a lone voice in the stands broke the tension by bellowing, “C’mon Venus, let’s see the magic.” This run of hers – at her 17th Australian Open – is nothing less. On the way off the court Williams wrapped her arms around herself at the sheer brilliance of it all, and nobody present could fault the sentiment.

Appearing not long after Williams on centre court was her compatriot Vandeweghe, who is quite used to following tough acts. The world No35’s mother Tauna was an Olympic swimmer, her uncle Kiki a 13-year NBA veteran, grandfather Ernie a New York Knicks star and her grandmother Colleen Kay Hutchins was Miss America in 1952. Try cracking a spot in that trophy cabinet.

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Well, now she has a decent chance after beating Muguruza in straight sets, adding her dismissal of the tournament’s seventh seed to those of the 15th and first. Vandeweghe’s semi-final clash with Williams will be the furthest she has gone in a grand slam in 10 years of trying, and for its total unlikeliness means that no matter the result it will be an American fairytale.

From the outset Vandeweghe took control of this match, hovering on level terms until it was 3-3 and Muguruza stumbled into a nightmare service game. The Spaniard battled away for 10 minutes of physical and emotional torture until her opponent finally put her out of her misery. The knock on Vanderweghe has always been her lack of consistency, but this was a level-headed and even-handed performance throughout.

The American took the first set in 56 minutes, hitting 19 winners to 12 and dominating for extended periods. Relentless pressure brought nine break opportunities to Muguruza’s one. That momentum rolled into a double break to start the second set, which meant an unassailable 3-0 lead after 12 minutes.

At the changeover Muguruza’s eyes darted towards the stands in search of inspiration but it never came. Last season’s French open champion was annihilated 6-0 in 28 minutes in the end, wrong-footed and outplayed in a crushing loss. “I really wasn’t feeling that great out there funnily enough,” Vandeweghe said afterwards. If that’s true, and she really fires, both Williams sisters might have a battle on their hands here.