Chelsea moved to the top of the Women's Super League as they fought back to beat West Ham United after Arsenal overcame title rivals Manchester City.
Tottenham also came from behind to win away from home as Kit Graham's superb quickfire double beat Bristol City.
Manchester United, Everton and Birmingham City were all 2-0 winners at home in Sunday's remaining matches.
Liverpool's loss at Birmingham extended their winless start and the Reds slipped to the bottom of the table.
Brighton and Bristol City also remain winless after the first five rounds of games and both dropped below Marta Tejedor's West Midlands side, who claimed their first league win with their first WSL goals.
- Match reports: Arsenal 1-0 Man City
- Birmingham City 2-0 Liverpool
- Bristol City 1-2 Tottenham
- Everton 2-0 Brighton
- Man Utd 2-0 Reading
- West Ham 1-3 Chelsea
All change at the top of the WSL
Manchester City began Sunday's action at the WSL's summit, with a 100% league record, but they were beaten by the Netherlands star Vivianne Miedema's only goal of the game for Arsenal at Meadow Park.
At one stage in a busy afternoon, Chelsea looked set to end the day in third as they trailed at West Ham to Adriana Leon's effort, with the Canada forward netting from her first touch after coming off the bench.
But Emma Hayes' side, who had hit the woodwork through England duo Beth England and Millie Bright, showed their class to eventually win comfortably at Rush Green.
Wales' Sophie Ingle found the top corner, Ji So-Yun scored a brilliant long-range goal and Drew Spence made it 3-1 in stoppage time.
The result left Chelsea as the only unbeaten side in the WSL after five rounds of fixtures, one point clear of Arsenal and Man City, who slipped to third.
A brighter note for Nick Cushing's team saw England striker Ellen White make her debut, returning from injury to play competitively for the first time since her six goals at this summer's World Cup.
Promoted pair continue to impress
Manchester United and Tottenham both earned their third wins from five WSL games since securing promotion last term, as they continue to look unlikely to be candidates for a return to the Championship.
The Red Devils were 2-0 winners over Reading thanks to Kirsty Hanson's far-post volley and Jess Sigsworth's cool second from a swift late counter.
Spurs had to come from behind at Bristol City, after Abi Harrison had fired the West Country side ahead in the first half.
Kit Graham - a summer signing from Charlton - netted her first two league goals for Spurs in quick succession to turn the game around in the space of two second-half minutes.
Sophie Baggaley later saved a Rachel Furness penalty as Spurs missed the chance to go 3-1 up, but they defended well late on to secure three points, as the Robins dropped to 10th.
Liverpool's early-season struggles continue
Joining United and Spurs on nine points from a possible 15 are fifth-placed Everton, following their 2-0 win over Brighton.
Willie Kirk's side led through Chloe Kelly's fourth goal in five WSL games and Esme Morgan headed in from a corner to ensure the victory.
That left Hope Powell's Brighton in 11th, above bottom side Liverpool by a point.
The Reds were beaten as Birmingham scored in each half at Damson Park, with England's Lucy Staniforth providing the early first - headed in by Kerys Harrop - before scoring the second on 83 minutes.
That defeat - Liverpool's fourth of the season - left the two-time WSL champions appearing set for a difficult season battling against the threat of relegation, with almost a quarter of the campaign gone.
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