Johanna Konta, who was drowning outside the world’s top 150 two years ago, looked every inch a potential grand slam champion in booking a quarter-final against Serena Williams with another excellent performance to beat Ekaterina Makarova 6-1, 6-4 in searing conditions on Margaret Court Arena on day eight.

Nadal through to Raonic quarter-final Rafael Nadal beat Gaël Monfils 6-3, 6-3, 4-6, 6-4 in a tense match on Monday to reach the Australian Open quarter-finals. Nadal has not reached the last eight in a major since the 2015 French Open and celebrated extravagantly after winning in two hours and 56 minutes at the Rod Laver Arena. The 30-year-old was rattled when Monfils rallied in the fourth set, but the 14-times grand slam champion was then clinical to keep his pursuit of a 15th major title alive. Nadal will meet third seed Milos Raonic for a place in the semi-finals.

“I’m really happy to have come through that,” she said courtside of the hour-and-nine-minute victory that looked like being a lot quicker when she brushed the Russian aside in the first set. “I came out playing at a higher level than she did but she was able to pull herself back into the match and made it really difficult for me. I just had to trust myself. At least it wasn’t three hours like when we played last year.”

Konta went on to reach the semi-finals then, losing to the eventual winner, Angelique Kerber – who was bundled out of this year’s tournament on Sunday night.

Blocking her way to that stage this time is six-time champion Williams, who earlier took an hour and 45 minutes in the killing heat on Rod Laver Arena to break down 16th seed Barbora Strýcová 7-5, 6-4.

“It was really good for me to win on probably not my best day,” Williams said later. As for Konta, the world No2 and new tournament favourite said, “I have watched her game a lot. She’s been playing really well. She has a very attacking game. I know her game pretty well. I look forward to it. I have absolutely nothing to lose in this tournament. Everything here is a bonus for me.”

Konta said of the prospect of playing Williams for the first time, “Believe it or not, that’s going to be an incredible experience for me. She was one of the players I watched growing up. It’s an incredible honour and I can’t wait to share a court with her. Once out on court, everyone is out to compete and give their best, but I will definitely cherish every single minute.”

She will take her best tennis into the quarters if she can replicate her form of Monday.

The on-court temperature when they began shortly after 1pm was close to 100F, with not a wisp of a breeze for relief. Both players retreated to the shadowed cool at either end whenever the opportunity arose and played with the sort of contained discipline that best husbands energy. The points, generally, were short, although old instincts surfaced and drew the combatants into extended struggles.

It could hardly have started better for Konta. The world No9 won the first three games inside 10 minutes and looked as commanding as she had in her impressive progress to the fourth round – but she knew from having played Makarova at this stage of the tournament a year ago that it would not be a stroll. That time, Konta won 8-6 in the third.

On Monday, the gap between Konta and the 30th seed was more apparent. The favourite served out the first set in only 24 minutes, and Andrew Castle was moved to describe it as “utter brilliance”.

He was not wrong. Konta’s serve again underpinned her dominance. She served five aces and was landing eight out of 10 first time. Her back-up strike was just as effective, giving Makarova no peace when defending, and she crumbled under the sustained, measured onslaught. At no time did Konta lose the shape of her game or focus on a plan she will have spent hours devising.

Williams, too, looked good earlier but took nearly an hour to go a set up against Strýcová, who saved eight set points. Her second set was more straightforward and it is clear she remains favourite, after the not altogether surprising exit of world No1 Kerber, who beat her in the final last year. It has not been a safe tournament for world No1s.

Makarova got on the board early in the second, determined not to go quietly: 6-1 is a not altogether rare score in the women’s game, even at this stage of a slam. Then followed the inevitable fightback.

Konta fell 4-1 down before taking five games in a row and served for the match. However, she had to save three break points and did so with the sort of nerveless tennis we have come to take for granted.

She got to deuce with her ninth ace and to match point with another – but Makarova would not go away, saving with a deep forehand to the deuce corner. Konta got back to match point, hitting hard to the same place at the other end, then sealed it after a tense rally, when Makarova could not control Konta’s fierce volley and put her forehand wide.

The concluding set had taken nearly twice as long as the first, a tribute to the fighting spirit of the loser, as well as the determination of the winner.

Konta’s next assignment will probably be even tougher.