Emily Fox, who had Arsenal's best chance, goes close with a header against Everton.Photograph: John Sibley/Action Images/Reuters

Arsenal dropped points at home in the Women's Super League as they were held to a goalless draw by injury-hit Everton in front of 25,000 fans at the Emirates Stadium.

Jonas Eidevall's side, who face Bayern Munich away from home in the Women's Champions League on Wednesday, saw the majority of the ball but lacked the creative spark to break through Everton's defensive wall. The United States right-back Emily Fox went closest for the home side but her effort struck the woodwork.

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Arsenal had won all 10 of their previous home fixtures against Everton since the WSL was founded in 2011. For Everton, who had endured a difficult start to the season after losing key players - the Italy midfielder Aurora Galli and the Spain midfielder Inma Gabarro - to season-ending anterior cruciate ligament knee injuries in their opening two games of the season, the draw and first point of the season will be a huge boost.

For Arsenal, the result will have been even more frustrating with the news that their title rivals, Manchester City, secured a 2-0 home victory over West Ham United in Sunday's earlier kick-off. Gareth Taylor was able to rest last season's WSL Golden Boot winner Khadija Shaw and the WSL's all-time leading scorer Vivianne Miedema from his starting line-up, with an eye on Wednesday's home game against defending European champions Barcelona, but his team still managed to avoid slipping up against Rehanne Skinner's winless side.

The England winger Lauren Hemp and the Australia forward Mary Fowler were on the scoresheet for City, who gave the Netherlands midfielder Jill Roord her first start since January, as she continued her comeback from her ACL injury. The France forward Viviane Asseyi did have the ball in the net in the second minute for the visitors, with the scoreline goalless, but her effort was ruled out for offside. Replays appeared to show she had been in an onside position.

Elsewhere, Liverpool picked up their first victory of the campaign in dramatic fashion as the Austria midfielder Marie Hobinger scored a 95th-minute penalty to give them a gripping 3-2 win away at Tottenham Hotspur. The result also saw Liverpool remain unbeaten after their opening three fixtures, while Tottenham lost for the first time this term.

In Sunday's 3pm kick-off, promoted Crystal Palace recorded their first win in the WSL as they deservedly beat Leicester City 2-0. Annabel Blanchard scored both goals for Laura Kaminski's side, the first a delightful team goal that she rounded off with a neat finish, and the second a calmly converted penalty. Both goals came in the second half, as the visitors impressed, with their on-loan Chelsea midfielder Lexi Potter in particularly good form.

That defeat meant that Leicester have not won a WSL match since 18 February, a run of 11 consecutive league games stretching back towards the middle of last season.

In the Women's Championship, leaders Charlton Athletic maintained their unbeaten start after scoring two late goals to earn a 3-3 draw at home to Sunderland. They are just a point above the surprise package Durham, who are second in the table after a 1-0 win away to Newcastle United. There were also wins for Birmingham City and Bristol City, while Isobel Goodwin scored four goals for London City Lionesses as they beat struggling Portsmouth 5-1.