Notts County are ahead of Liverpool on goal difference at the top of the Women's Super League after a 0-0 draw at Meadow Lane.
Manchester City collected their first points of the season with a 1-0 win at Arsenal.
Birmingham City also picked up their first league win of the campaign, a 2-1 success against Chelsea.
Everton were denied victory by Nikki Watts' equaliser in a 1-1 draw with Bristol Academy.
Notts County 0-0 Liverpool
Notts had the better of the first half but almost went behind when striker Natasha Dowie landed a 19th-minute header on top of the bar.
Magpies striker Jess Clarke had a 37th-minute effort superbly saved by keeper Libby Stout.
But, though County winger Dunia Susi went close on a couple of occasions in the second half, neither goal was seriously threatened.
Arsenal 0-1 Manchester City
Toni Duggan chested in a 12th-minute Krystle Johnston cross to put City in front.
Arsenal hit back but rarely looked likely to force a first-half equaliser as the visitors pressed their opponents in every area of the pitch.
City started the second half well and Duggan had a low cross-shot saved by the outstretched foot of goalkeeper Emma Byrne.
The striker should have doubled her tally when clean through in the 66th minute, but her chip over Byrne sailed wide of the far post.
That miss almost proved costly when Arsenal substitute Freda Ayisi forced keeper Karen Bardsley into a smart save.
Bardsley did even better seven minutes from time, diving full length to turn striker Kelly Smith's 20-yard drive on to the bar.
Birmingham City 2-1 Chelsea
Birmingham went ahead after only six minutes, right-back Chelsea Weston looping over a high cross that dropped just inside the far post.
Former Birmingham striker Eni Aluko had a good effort saved by goalkeeper Rebecca Spencer as the visitors responded immediately.
Chelsea midfielder Katie Chapman then sent a 25-yard drive against the bar.
But, seconds from half-time the home side were denied a second goal when Mel Lawley's shot was brilliantly cleared off the line by full-back Claire Rafferty.
Chelsea were back on level terms five minutes after the interval, defender Hannah Blundell shooting in from midfielder Dani Buet's corner.
Birmingham captain Karen Carney had a penalty saved by the diving Christiane Endler on the hour.
But, the home side grabbed the winner when Jo Potter headed home a Kirsty Linnett cross 12 minutes from time.
Everton 1-1 Bristol Academy
Both goalkeepers had to pull off early saves before winger Watts went close with a curling 31st-minute shot that struck the Everton post.
Everton went in front in the final minute of the first half, striker Nikita Parris lobbing the ball home.
Spanish striker Laura Del Rio fluffed an equalising chance when she fired a 52nd-minute penalty over the bar.
But Bristol deservedly drew level when Watts headed in captain Corinne Yorston's 71st-minute cross.