But they managed to get that game over the line and did so again on Sunday, as Harder scored from the spot after Lisa Robertson handled the ball.
Birmingham came close in the dying minutes of the game, but a fingertip stop from Berger kept out Emily Whelan’s shot from the edge of the box and secured the win.
Manager Darren Carter said he didn’t have “too many qualms” about the penalty decision but he was “gutted that it’s cost us at least a point”.
He added: “To lose the game on a penalty, and then to have a couple of chances at the end – we’re gutted, because I think there was something there for us.”
The WSL title remains in Chelsea’s own hands going into their final fixture next Sunday, at home to Manchester United – and they will be champions before then if Arsenal lost at home to Tottenham on Wednesday.
B’ham City Women
32CowieBooked at 35minsSubstituted forWhippat 67′minutes
3ScottBooked at 90mins
8RobertsonBooked at 43minsSubstituted forWhelanat 86′minutes
11PennockSubstituted forSmithat 67′minutes
30BergerBooked at 90mins
7CarterSubstituted forAnderssonat 64′minutes
5IngleSubstituted forJamesat 64′minutes
23HarderSubstituted forSpenceat 82′minutes
20KerrSubstituted forMjeldeat 86′minutes
9EnglandSubstituted forCuthbertat 45′minutes
Match ends, Birmingham City Women 0, Chelsea Women 1.
Second Half ends, Birmingham City Women 0, Chelsea Women 1.
Harriet Scott (Birmingham City Women) is shown the yellow card for a bad foul.
Niamh Charles (Chelsea Women) wins a free kick on the right wing.
Foul by Harriet Scott (Birmingham City Women).
Ann-Katrin Berger (Chelsea Women) is shown the yellow card.
Attempt missed. Lucy Whipp (Birmingham City Women) right footed shot from the right side of the box is high and wide to the right following a corner.
Corner, Birmingham City Women. Conceded by Magdalena Eriksson.
Attempt saved. Emily Whelan (Birmingham City Women) left footed shot from the centre of the box is saved in the top centre of the goal.
Corner, Birmingham City Women. Conceded by Jonna Andersson.
Offside, Chelsea Women. Niamh Charles tries a through ball, but Lauren James is caught offside.
Substitution, Birmingham City Women. Emily Whelan replaces Lisa Robertson.
Substitution, Chelsea Women. Maren Mjelde replaces Sam Kerr.
Substitution, Chelsea Women. Drew Spence replaces Pernille Harder.
Guro Reiten (Chelsea Women) wins a free kick in the defensive half.
Foul by Lisa Robertson (Birmingham City Women).
Attempt blocked. Veatriki Sarri (Birmingham City Women) left footed shot from outside the box is blocked.
Foul by Erin Cuthbert (Chelsea Women).
Christie Murray (Birmingham City Women) wins a free kick in the defensive half.
Attempt blocked. Erin Cuthbert (Chelsea Women) right footed shot from outside the box is blocked. Assisted by Magdalena Eriksson.