Great passing backhand from Ash Barty. Jessica Pegula gets a racquet to it but can't engineer any sort of shot from there. Break point number four in this service game.

Ace! That'll do it. But Jessica Pegula needs to string a couple of points together now.

Ash Barty isn't letting go of this... she brings up a third chance to break in the opening game of the second set.

That's a lovely backhand winner from the American! She fends off the break again.

More slice than a loaf of bread on that Ash Barty backhand and Jessica Pegula can't pick it up. Another chance to break for the Australian.

Barty wraps a forehand return low into the net and Pegula survives that break. Deuce.

Ooh! Unlucky. The American reads Ash Barty's first smash and then the second too, but can only coax it narrowly wide of the mark. Break point for the top seed.

Right then, can Jessica Pegula find a way back into this match?

"Aussie, Aussie, Aussie" is the cry. Ace is the move. A one-set lead is the result.

So Ash Barty will serve for the opening set.

The world number one whips down a leaping second serve that Jessica Pegula pops long.

Pegula can only poke the next serve wide and that's three set points.

Ash Barty takes a double break!

Nice depth on the world number one's groundstrokes and Jessica Pegula can only cup a backhand into the tape.

A sigh from the crowd as Ash Barty lumps a forehand long. Applause for the Australian when she forces Jessica Pegula into doing the same.

Pegula wriggles towards the net but a bullet of a Barty backhand bounces off the American's strings and drops beyond the baseline. She can't pick up the next one, either.

All of a sudden it is break point Barty.

The Australian recovers with a whipping second serve and edges to 40-30. A screamer of a first serve is followed up with a meaty forehand as Ash Barty holds.

Ash Barty isn't quite at her free-flowing best so far, despite being a break up. A wayward backhand drifts long and that's 15-30.

Oooh! Ash Barty skips around a short ball and you think surely it only means one thing... but she pops the forehand into the tramlines. A big hold for Jessica Pegula.

A few little murmurs around Rod Laver Arena as this match settles into its flow. Jessica Pegula tries to come forward and is undone by Ash Barty. That's deuce.

Ash Barty is struggling close this out.

She flicks a backhand into the net. But eventually, the relieved world number one gets over the line to hold.

A leaping second serve from Ash Barty comes up trumps as Jessica Pegula swats it into the tape. Deuce.

Another error from the world number one, that's 12 for the match. And it means a chance to break back for Jessica Pegula.

Oh, wow. Ash Barty watches the fluff drop out of the Melbourne sky and swats it away with a forehand volley around chest height - unbelievable composure and execution.

She's been a little off on a couple of others, though. Deuce once more.