Birmingham avoided defeat for just the third time this Women's Super League season, but their draw against Everton does little to boost their chances of avoiding relegation.
The Blues had to dig in to claim just a fifth point of the campaign against a superior Toffees side, who made the game's best chances.
However, City remain seven points from safety with just four games remaining.
Everton are now safe from the drop, with the draw taking them to 18 points.
They should really have won this game on the balance of play and number of opportunities, which included two saved efforts from the lively Kenza Dali in the opening quarter of the game.
Toni Duggan had the best of them when she was gifted possession through a dire Louise Quinn back pass and rounded the keeper only to then fire wide from an angle.
Izzy Christiansen also saw a long-range shot tipped over by home goalkeeper Emily Ramsey.
Birmingham only really started to threaten late in the game and even then could only produce half-chances.
With just four games to go, two of which see them face leaders Chelsea and Champions League-chasing Manchester City, spending next season in the Championship is all but assured.