City fell behind after four minutes when Claudia Walker produced a fine strike from 25 yards that Marie Hourihan could do little about but Nick Cushing’s side soon assumed control.
They pressed the home side high up the field, not letting them settle on the ball for a second, and when they were in possession they moved it swiftly and inventively.
Everton were struggling to contain them and Bremer’s header, which was saved by Durack, was a sign of things to come, as three goals in eight minutes turned the game in City’s favour.
Steph Houghton, superb throughout, fired in a free-kick from distance that gave Durack no chance, and a minute later Nikita Parris’ backpost header gave City, backed by around 150 travelling supporters, a deserved lead.
Bremer made it 3-1 by planting a brave header past the onrushing Durack – her first goal in a City shirt since her summer move from Lyon - as City continued creating chances at will.
They were in complete control of the match but then came the moment that overshadowed their performance. Bremer, looking to get on the end of a throughball, was challenged by Everton defender Gabrielle George and immediately went down in clear discomfort. Those around her, distressed by what they had seen, called for medical assistance and after an eight-minute delay she was stretchered off for treatment. She will be assessed and the extent of her injury will become clearer in the coming days.
City’s level remained high, though. Nikita Parris skipped past one challenge and produced a powerful effort from 10 yards but Durack was equal to it, and the Everton ‘keeper then denied Jane Ross with seconds remaining before the break.
The second-half saw the pattern continue. Campbell’s free-kick was saved by Durack, who then palmed away Parris’ effort, before Houghton’s backpost header drifted just wide of the upright.
But City lost their rhythm after that and the game suffered. Their passing lost its purpose and Everton, sensing an opportunity to get back in the match, duly obliged when Magill pulled one back after 65 minutes, poking home after City failed to clear a free-kick from the right.
But Cushing’s side stood firm, making it nine points from a possible nine and keeping the pressure on Chelsea, who won earlier in the day, at the top of the WSL table.
This was a decent away performance from City – but the night will be remembered for an unfortunate incident rather than the moments of attacking quality they produced.