An increasingly comfortable Aryna Sabalenka powered into the final of the Australian Open by seeing off her good friend and the 11th seed, Paula Badosa, under the roof on Rod Laver Arena, as she continued her pursuit of a third straight title here.

The Belarusian’s forehand and serve proved too powerful despite Badosa’s early resistance and the world No 1 pulled away in the second set to win 6-4, 6-2 in 86 minutes.

Related: Australian Open semi-finals: Madison Keys v Iga Swiatek; Sabalenka beats Badosa – live

Sabalenka took time to find her range and for much of the first set this match appeared on a knife-edge as an avalanche of unforced errors kept her opponent in it. But after the roof closed midway through the set, the defending champion elevated her game and Badosa had few answers.

Sabalenka said she played an “incredible match”, but only after the turning point in the first set. “When I broke her twice, and I was 3-2 up, I felt: ‘OK, I’m back’. My game much better and I was like: ‘OK, now it’s time to step in.’”

Badosa was a surprise participant in the semis after her upset of the American Coco Gauff in the quarter-finals. But in the early stages of her first appearance in the last four of a grand slam, the Spaniard looked the better player. She broke Sabalenka in her first service game and had ­multiple chances to take a 3-0 lead in the first set.

“Somehow I was able to turn around the match in that crucial game,” Sabalenka said. “That was a super-tough match against a friend, super happy for her, to see her on her highest level.”

Sabalenka arrived slowly but she left in a rush. Half an hour into a ­compelling duel the ­scoreboard showed 2-2, but the favourite ­eventually took control and claimed the first set in 53 minutes. The second took 33.

After an uneven tournament this was a statement display by Sabalenka, who is the first to reach a third consecutive final here since Serena Williams in 2017.

Badosa said there was little she could do: “She played the best match, not even of the week, from the last months. So if she plays like this we can already give her the trophy.”

Although the match was over more quickly than the crowded Rod Laver Arena would have liked, it was a ­terrific ­display on the ­tournament’s day to celebrate women and girls in the sport. The umpire and ball kids were all female and the match between two friends was contested in good spirits.

One moment in the second set highlight their rapport. Badosa stumbled and fell while chasing a forehand, her racket spraying across the court. For a moment she looked injured and Sabalenka showed ­concern. But Badosa gave her the signal she was fine, smiling at the embarrassment and later mocking her own clumsiness.

Recognising she was well beaten, Badosa celebrated when she held serve in the penultimate game and looked to the heavens and expressed thanks. The pair embraced warmly at the net at the conclusion.

Sabalenka is confident they will remain friends. “I’m sure she’ll hate me for the next day or two, I’m OK with that, I can handle that. And after that, I think we’re back to be friends, back to go out together shopping,” she said. “I promise, Paula, we go ­shopping and I pay for whatever she wants.”

When Badosa was told what Sabalenka had promised, she said she would think about what she wanted. “It’s going to be something really expensive, because now she ­doubled the prize money [by ­reaching the final] so she won’t have the problem for that.”