Tomljanovic is a scrapper and she's getting some punches back.

She moves to advantage but is stopped by a Dart volley. The Brit has a serious spring in her step.

Eventually Tomljanovic gets over the line and she manages a wry smile.

She isn't smiling inside, I can assure you.

Harriet Dart to serve for the match...

Deep breathes from Tomljanovic between serves. That tells us she's feeling it.

Dart continues to press, forcing deuce when Tomljanovic dumps a forehand into the net.

Can the Brit wrap it up here?

One game away.

Harriet Dart is the coolest cucumber in the whole place.

Another confident service game sees Dart hold to 15, with Tomljanovic again making an error at the end of it.

She's been suffocated by Dart.

They are dancing in the seats of Glasgow. And that's even without The Proclaimers banging out over the PA system.

It's a real Darty party.

A double break for Harriet Dart!

The Brit can't take either of the first two opportunities as Tomljanovic rallies, but it is third time lucky after a poor error from the Aussie.

Dart can only loop a return from a serve high and Tomljanovic inexplicably thumps the volley wide.

The facepalm says it all.

That hands over a third break point...

This time Dart gets it when a backhand from Tomljanovic clips the net and flies wide.

Tomljanovic is looking a little rattled. Balls are being sprayed left and right now. Another wayward return sets up two break points to Dart...

Solid, very solid. Comfortable hold for Dart, who is scurrying around the court like her life depends on it. Tomljanovic goes wide with a forehand and the Brit maintains her advantage.

Harriet Dart guzzled an energy gel at the changeover. Might be worth lobbing a few back behind her to the band.

Tremendous energy on and off court from the Brits.

Russell Fuller
BBC tennis correspondent

There were 17 winners for Harriet Dart in that first set, and crucially she did not go back into her shell after her 5-2 lead evaporated.

Three thousand-plus fans are now contributing to the best atmosphere of the week so far.

The face of Ajla Tomljanovic says it all. Mean and moody as she tries to turn this match back in her favour.

That focus enables her to race 40-0 ahead and, after another double fault checks her rapid progress, Dart sprays a forehand east.

Britain still a set and a break up in this must-win match.

Another superb hold by Harriet Dart. You really have to laud her ability today to fight back positively from the set-backs she has suffered.

The Brit consolidates the break by sealing the game with a rare ace.

Image source, Getty Images

Oh my! Tomljanovic fetches a backhand return from downtown and turns it into a winner.. break point.

But Dart scraps hard again, drags her opponent into another slugfest of a rally and the winded Aussie dumps a backhand into the net.

Back to deuce.

Big moment. Dart leaves the jar ajar at 15-30 and then misses a first serve.

Tomljanovic licks her lips, she fancies attacking the Dart second serve.

But the Aussie goes big and drops her head in disappointment. She knows.

From 30-30, Dart moves 40-30 ahead as she looks to consolidate.

Then, disaster! A double fault. Deuce...

The first break point is saved by brave play from the baseline, but Dart reasserts herself to take the second.

She moves forward and sticks away a volley before skipping away to her seat in celebration.

In a must-win match for GB, Dart leads by a set and a break!

Oooh! Pressure starting to show on Tomljanovic. A double fault draws gasps from the crowd and brings up two break points for Dart...

That was pretty special from Harriet Dart.

She's been a player reborn this year and we're here for it.

Such a high level throughout.

Can she maintain it in the second set?

Tomljanovic to serve first...

She needs only one. Harriet Dart takes the first set for Great Britain.

One hour and eight minutes that set took. This is a tussle!

Such brilliant, aggressive play from Harriet Dart to earn herself three set points.

Gigi Salmon
BBC Sport tennis commentator

What a point from both players!

The court coverage from both players was exceptional and the finish from Dart... she remained cool to use her hand speed to whip the winner behind Tomjlanovic.

Image source, Getty Images

Exquisite play from both players on the next point, but Dart finishes it with aplomb.

Tomljanovic gets the mini-break back, but then immediately concedes the next two points.