WSL: Tottenham, Manchester City, Everton & West Ham win, Chelsea held
Chelsea needed a stoppage-time equaliser to rescue a point at Brighton, while Manchester City and Everton made it two wins from two this season in the Women's Super League.
Brighton looked set for an upset when Aileen Whelan opened the scoring, but Chelsea substitute Adelina Engman levelled late on to make it 1-1.
City and Everton beat Reading and Bristol City respectively, both 2-0.
Tottenham beat Liverpool for their first win and West Ham beat Birmingham.
Late equaliser spares Blues from shock defeat
In a rather uneventful opening 80 minutes it seemed like Brighton and Chelsea's match at Crawley was destined for a goalless draw.
But when Aileen Whelan put the hosts in front with six minutes to go with a well-placed shot, it looked like the visitors were heading for a surprise loss.
Substitute Engman was on hand to spare Chelsea's blushes, however, and the Blues nearly thought they had found a winner in the closing seconds as Maria Thorisdottir hit the post from a late free-kick - but the flag had already been raised for offside.
Bremer steps up for injury-hit City
Manchester City boss Nick Cushing could not have asked for a better start to his side's Champions League campaign on Thursday, beating Swiss side Lugano 7-1 away from home.
And last year's WSL runners-up were in fine form once again, maintaining their 100% record thanks to two goals from Pauline Bremer.
The Germany international now has four goals from her past two games and could have had a hat-trick, but saw a glancing header come back off the post.
It was not all good news for the visitors on Sunday, however, as City announced before kick-off that England international Georgia Stanway will be sidelined with a hamstring injury for the next six weeks.
She joins the away side's already extensive injury list which also includes fellow Lionesses Ellen White and Karen Bardsley.
First wins for Spurs and West Ham and screamers at Everton
Chloe Kelly scored two goal-of-the-season contenders in as many minutes to give Everton a routine win over Bristol City.
The Toffees won just three games in the WSL last season and finished second-from-bottom, but have now won two from two this campaign thanks to Kelly's excellence, and 21-year-old could have had a hat-trick, seeing a second-half strike ricochet off the bar.
Elsewhere, there were first wins of the season for newly promoted Tottenham and last season's FA Cup finalists West Ham.
Tottenham were awarded a penalty when Rachel Furness was brought down in the box by Becky Jane just before half-time and the Northern Ireland international made no mistake from the spot, sending Liverpool goalkeeper Anke Preuss the wrong way to score her first Spurs goal.
Liverpool's Niamh Fahey saw a straight red card for a foul on Rosella Ayane midway through the second half as the Reds succumbed to a seventh loss in their past nine matches in the WSL.
Meanwhile, West Ham held on as Canada international Adriana Leon's first-half strike was enough to beat Birmingham 1-0.
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