Victory sees Liverpool rise to fourth in the table, although they've played a game more than Manchester United.
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Defeat for Bristol City means they miss out on a chance to keep their hopes of safety alive as they remain seven points behind second-bottom West Ham.
Getty ImagesCopyright: Getty Images
FULL-TIME
Bristol City 0-1 Liverpool
Liverpool get a narrow victory over the line at Ashton Gate - and with that Bristol City's hopes of remaining in the top flight are all but mathematically over.
They trail West Ham by seven points with three games left and have played a game more than the second-bottom Irons.
They might even go down tomorrow if West Ham beat Manchester City.
Post update
Bristol City 0-1 Liverpool
Bristol City attempted 369 passes in this game, their highest total in a single match in the Women's Super League this season.
It hasn't been enough to get what they need, though.
Post update
Bristol City 0-1 Liverpool
The injured Liverpool player is back up and we're into the final minute of added time.
We'll probably have some more added on for that injury.
SUBSTITUTION
Bristol City 0-1 Liverpool
Bristol City make their final change as Abi Harrison replaces Jasmine Bull.
Post update
Bristol City 0-1 Liverpool
There's another stoppage now as a Liverpool player goes down.
INJURY TIME
Bristol City 0-1 Liverpool
Five minutes added at Ashton Gate. Five huge minutes for Bristol City.
Post update
Bristol City 0-1 Liverpool
Good effort!
Carrie Jones has a go from range and it's not too far away but Teagan Micah catches.
We've seen her score some audacious strikes before.
Post update
Bristol City 0-1 Liverpool
Play has stopped again as a Liverpool player goes down with a head injury.
As it stands Bristol City are missing out on a chance to save their season.
SUBSTITUTION
Bristol City 0-1 Liverpool
Another roll of the dice from Lauren Smith as she tries to find a way back for Bristol City.
Mari Ward replaces Emily Syme.
Post update
Bristol City 0-1 Liverpool
We're going to have a late stoppage as Shae Yanez has gone down holding her leg and needs some treatment.
Post update
Bristol City 0-1 Liverpool
Argh.
Liverpool nearly seal the victory as the ball is pulled back towards Sophie Roman Haug as the Reds break down the left-hand side, but she can't get to Mel Lawley's pass in time.
Post update
Bristol City 0-1 Liverpool
Liverpool are happy to just play out from the back and control possession now.
Bristol City have been shut out in the second half.
Post update
Bristol City 0-1 Liverpool
Ooooh!
Missy Bo Kearns goes for goal with a free-kick from a tight angle.
Shae Yanez hadn't been anticipating it but manages to scramble back in time to make the save.
SUBSTITUTION
Bristol City 0-1 Liverpool
Liverpool make two more changes.
Mia Enderby, who has come close to scoring on a couple of occasions, makes way for Melissa Lawley.
Lucy Parry also goes off and is replaced by Yana Daniels.
Post update
Bristol City 0-1 Liverpool
Will anyone find a way to change the scoreline?
Mia Enderby gets in behind the Bristol City defence but her near-post effort is turned behind by Shae Yanez.
Post update
Bristol City 0-1 Liverpool
What a chance that was!
Bristol City are gifted an opportunity to equalise as a mistake sees the ball drop to Amalie Thestrup behind the Liverpool defence, but Tagan Micah watches her shot and parries it away.
Post update
Bristol City 0-1 Liverpool
She just didn't get that right.
The Bristol City defence parts and it opens up a great gap for Mia Enderby to curl an effort towards the Vixens' goal, but she slices a good distance wide.
SUBSTITUTION
Bristol City 0-1 Liverpool
Liverpool take off goalscorer Marie Hobinger and captain Taylor Hinds.
Ceri Holland and Emma Koivisto replace them.
Post update
Bristol City 0-1 Liverpool
Bristol City have been muted in the second half.
They have had a few periods of possession but are yet to find a way to get in behind the Liverpool defence and make the most of their half-time introductions.
Live Reporting
Adam Millington
All times stated are UK
Getty ImagesCopyright: Getty Images 
Getty ImagesCopyright: Getty Images
Latest PostThat's all from us
FT: Bristol City 0-1 Liverpool
Thanks for tunining in this afternoon.
That's all from us, but we'll be back tomorrow for the rest of the weekend's Women's Super League games.
For now, click here to read the report and take a look below to see what it means for the table:
Victory sees Liverpool rise to fourth in the table, although they've played a game more than Manchester United.
Defeat for Bristol City means they miss out on a chance to keep their hopes of safety alive as they remain seven points behind second-bottom West Ham.
FULL-TIME
Bristol City 0-1 Liverpool
Liverpool get a narrow victory over the line at Ashton Gate - and with that Bristol City's hopes of remaining in the top flight are all but mathematically over.
They trail West Ham by seven points with three games left and have played a game more than the second-bottom Irons.
They might even go down tomorrow if West Ham beat Manchester City.
Post update
Bristol City 0-1 Liverpool
Bristol City attempted 369 passes in this game, their highest total in a single match in the Women's Super League this season.
It hasn't been enough to get what they need, though.
Post update
Bristol City 0-1 Liverpool
The injured Liverpool player is back up and we're into the final minute of added time.
We'll probably have some more added on for that injury.
SUBSTITUTION
Bristol City 0-1 Liverpool
Bristol City make their final change as Abi Harrison replaces Jasmine Bull.
Post update
Bristol City 0-1 Liverpool
There's another stoppage now as a Liverpool player goes down.
INJURY TIME
Bristol City 0-1 Liverpool
Five minutes added at Ashton Gate. Five huge minutes for Bristol City.
Post update
Bristol City 0-1 Liverpool
Good effort!
Carrie Jones has a go from range and it's not too far away but Teagan Micah catches.
We've seen her score some audacious strikes before.
Post update
Bristol City 0-1 Liverpool
Play has stopped again as a Liverpool player goes down with a head injury.
As it stands Bristol City are missing out on a chance to save their season.
SUBSTITUTION
Bristol City 0-1 Liverpool
Another roll of the dice from Lauren Smith as she tries to find a way back for Bristol City.
Mari Ward replaces Emily Syme.
Post update
Bristol City 0-1 Liverpool
We're going to have a late stoppage as Shae Yanez has gone down holding her leg and needs some treatment.
Post update
Bristol City 0-1 Liverpool
Argh.
Liverpool nearly seal the victory as the ball is pulled back towards Sophie Roman Haug as the Reds break down the left-hand side, but she can't get to Mel Lawley's pass in time.
Post update
Bristol City 0-1 Liverpool
Liverpool are happy to just play out from the back and control possession now.
Bristol City have been shut out in the second half.
Post update
Bristol City 0-1 Liverpool
Ooooh!
Missy Bo Kearns goes for goal with a free-kick from a tight angle.
Shae Yanez hadn't been anticipating it but manages to scramble back in time to make the save.
SUBSTITUTION
Bristol City 0-1 Liverpool
Liverpool make two more changes.
Mia Enderby, who has come close to scoring on a couple of occasions, makes way for Melissa Lawley.
Lucy Parry also goes off and is replaced by Yana Daniels.
Post update
Bristol City 0-1 Liverpool
Will anyone find a way to change the scoreline?
Mia Enderby gets in behind the Bristol City defence but her near-post effort is turned behind by Shae Yanez.
Post update
Bristol City 0-1 Liverpool
What a chance that was!
Bristol City are gifted an opportunity to equalise as a mistake sees the ball drop to Amalie Thestrup behind the Liverpool defence, but Tagan Micah watches her shot and parries it away.
Post update
Bristol City 0-1 Liverpool
She just didn't get that right.
The Bristol City defence parts and it opens up a great gap for Mia Enderby to curl an effort towards the Vixens' goal, but she slices a good distance wide.
SUBSTITUTION
Bristol City 0-1 Liverpool
Liverpool take off goalscorer Marie Hobinger and captain Taylor Hinds.
Ceri Holland and Emma Koivisto replace them.
Post update
Bristol City 0-1 Liverpool
Bristol City have been muted in the second half.
They have had a few periods of possession but are yet to find a way to get in behind the Liverpool defence and make the most of their half-time introductions.