Gemma Bonner’s first-half header ensured Manchester City leapfrog Chelsea and stay level with Arsenal at the top of the Women’s Super League, despite a resolute performance from a Liverpool team still searching for a first league win of the season.

“I’m still smiling,” said Liverpool manager Vicky Jepson. “The performance was there. Last week we saw Arsenal run the ball into the corner to waste time, this week we’ve seen City do it, that’s a huge compliment to our players and their work rate and effort.”

Liverpool have never won away to Manchester City in the WSL but their visit to the Academy Stadium was buoyed by the narrowness of their 1-0 defeat by the champions Arsenal the preceding Sunday. That the Gunners were hammering Bristol City 11-1 in the earlier kick-off will have no doubted added to a sense that something was achieved at Meadow Park, despite Jepson’s team still being winless and bottom of the WSL table.

Liverpool do seem to be improving. Their league defeats have been narrow ones. Just two have exceeded the one-goal margin (2-0 defeats to Manchester United and Birmingham the anomalies). But Manchester City presented a different kind of challenge. Where Arsenal have now conceded four times in eight games, offering teams a glimmer of hope at catching them out, City are rock solid. The only goal they have shipped was in a 1-0 defeat to Arsenal.

“We’ve been resilient and fought hard to make sure it was three points and not one,” said the manager Nick Cushing of the win. “One week you can win 1-0 the next week you can win 11-1,” he said after being told Arsenal’s result. “We’re just trying to make sure we get points and continue to push them.”

The threat of City was evident early on. A Keira Walsh shot, hit first time, was tipped over by Anke Preuss. Sophie Bradley-Auckland’s late recovery nicked the ball off the feet of Lauren Hemp as the youngster raced goalwards with just the keeper to beat.

The visiting team’s closest chance came when a goalmouth scramble saw Jade Bailey find Courtney Sweetman-Kirk but England striker Ellen White blocked her eventual shot.

Vicky Jepson’s Liverpool remain bottom of the table after narrow defeats to Manchester City and Arsenal. Photograph: Kate McShane/Getty Images

City broke the deadlock on the 20-minute mark, and it was beautifully simple. A 25-yard free-kick was floated on to the head of Bonner, a former Liverpool defender, by Caroline Weir who nodded in. White had the chance to double their lead shortly after, Walsh having snuck the ball between the lines to the forward but, forced wide, her shot from an acute angle was nudged past the far post by Preuss.

For City, every point matters. With Chelsea unbeaten, but with a game in hand after their match at Everton was called off due to a frozen pitch, Manchester City needed to take advantage of a chance to leapfrog the London club, to sit level with Arsenal on 21 points. Arsenal’s mammoth win though, means that they also needed goals. With 14 scored in their last three games, the likelihood of them punishing Liverpool was high, but with Bailey and Rhiannon Roberts sitting in front of the back four the home side struggled to penetrate.

Their solidity at the back gave the visitors confidence. And with 70 minutes on the clock they launched a period of sustained pressure on City’s resolute defence, a spell which culminated in a Bailey shot being acrobatically tipped over by Ellie Roebuck, and a scramble that saw Niamh Charles’ eventual header stopped at point-blank range by the young keeper.

“Two minutes’ extra time left and our players were still busting a gut to try and get something from it so there’s no stress here, there’s no worries in our camp,” said Jepson.

“Liverpool have improved performances and they had a positive performance against Arsenal so we knew they would come here trying to get something,” said Cushing. “We knew it was going to be dangerous. I just thought we lacked a little bit of control in the second half - a little bit of fatigue came in and we looked tired.

“We now go to Chelsea for a really important game next week. We want to make sure in the head-to-heads we are challenging so towards the end of the season we’re in the top two and challenging for a trophy.”