Becky Grey and Alex Bysouth
All times stated are UK
Goodbye
That's all from us but you can continue listening to BBC Radio 5 Live commentary by clicking the play icon at the top of this page.
If you need to catch up on the day's action so far, here's a reading list:
- British teenager Emma Raducanu won on her US Open main-draw debut
- Alexander Zverev hopes to 'challenge' Novak Djokovic after a composed opening win
- Czech fourth seed Karolina Pliskova powered past American Catherine McNally to reach the US Open second round.
'I am exceptionally proud'
And here is Ash Barty: "I was disappointed not to be able to play last year but this year with fans has made it all the better, the city is buzzing and it is nice to share this with everyone here today.
"I am exceptionally proud, we made the right decisions for us - we trained and got ready, came into this year with the attitude it was going to be a different adventure for us, but it has been really enjoyable right from the start."
On hitting balls with golfer Ian Poulter: "I do love playing golf, it is a hobby of mine, I haven't played as much as I would have liked, I come from a golfing family so it is nice to hit a few balls."
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Barty's second-round opponent was decided just as she wrapped up that victory.
She will face world number 78 Clara Tauson next. The Dane has just beaten France's Clara Burel 7-5 6-0.
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Naomi Broady
British player on BBC Radio 5 Live Sports Extra
She didn't look that happy, I wonder if sometimes you lose perspective as to how well your opponent is playing.
Game, set and match Barty
Barty 6-1 7-6 (9-7) Zvonareva
See AlsoUS Open LIVE: Alcaraz, Sinner, Raducanu, Swiatek, Boulter, Draper, Evans - live scores, results, order of playUS Open LIVE: Alexander Zverev vs Taylor Fritz - quarter-final live text & radio commentaryUS Open: Williams begins farewell with win over KovinicUS Open: Wozniacki beats Brady and Swiatek wins on day fiveAnd this one is good!
Vera Zvonareva loops her forehand long and world number one Ashleigh Barty is through to the second round.
The Russian put up some impressive resistance in that second set.
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Barty 6-1 6-6 Zvonareva*
Barty seemed to work out what shot to hit that time.
She comes in for a forehand volley and lightly taps it over the net to bring up her second match point.
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Naomi Broady
British player on BBC Radio 5 Live Sports Extra
She is just not affected by the slice at the moment, Zvonareva, she is staying patient and it is almost like Ash Barty doesn't know what shot to hit at the moment.
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Laura Robson
Former British number one on BBC Radio 5 Live Sports Extra
Ash Barty does not look happy with this situation...
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Barty 6-1 6-6 Zvonareva*
The crowd almost groans as Barty's forehand just stays inside the lines. Match point saved.
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Barty 6-1 6-6 Zvonareva*
Set point Zvonareva!
Barty's backhand goes long.
The Australian was so, so dominant. Now we could be going to a decider.
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Barty 6-1 6-6 Zvonareva*
It really felt like Barty was building through the lengthy rally, smelling blood. But no... her forehand goes into the net and we go on. 6-6.
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Barty 6-1 6-6 Zvonareva*
The Russian can't back it up as she is outpowered by Barty's forehand. 6-5 - match point to the Australian.
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Barty 6-1 6-6 Zvonareva*
Nope.
Zvonareva repays Barty for her earlier booming backhand down the line with one of her own and claws the break back. Back on serve at 5-5.
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Barty 6-1 6-6 Zvonareva*
A backhand into the net brings up 5-4 but if Barty can hold both her serves here she's into the second round.
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Barty 6-1 6-6 Zvonareva*
Lovely serving from Barty and her 11th ace of the match makes it 4-3.
The Australian's backhand winner down the line is perfect to go a mini-break up at 5-3.
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Laura Robson
Former British number one on BBC Radio 5 Live Sports Extra
How good was that spin from Ash Barty on the forehand side - she has such easy technique that it just makes it look like she was born this good.
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Barty 6-1 6-6 Zvonareva*
Break back secured. Zvonareva's shouts reach their highest pitch as she realises she's not got the measure of Barty in a lengthy rally.
Her forehand goes into the net and it's back on serve at 3-2.
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Barty 6-1 6-6 Zvonareva*
Zvonareva holds her first serve. Barty holds hers too, but then bats her forehand long to give the Russian an early break at 2-1 up.
Barty takes it to a tie-break
Barty 6-1 6-6 Zvonareva*
This is more like it.
All of a sudden Barty looks back to her best as she whips a forehand winner into the left corner for 40-15.
A serve out wide takes us to the tie-break.
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*Barty 6-1 5-6 Zvonareva
Ashleigh Barty has hit 16 unforced errors in this second set.
The 16th brings up 0-15 but she pulls off an impressive forehand winner for 15-15.
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