The second half, however, was a different story. Just one minute after the restart, London City equalised with a fortunate deflection off the post.
France international Grace Geyoro tried her luck from the edge of the box, and her effort rebounded off the post and into the path of Sanni Franssi, who had the simplest of tasks to tap home an equaliser.
The woodwork would then come to Palace's aid 20 minutes later, as London City were denied twice in two minutes.
Substitute Nikita Parris almost had an instant impact on 65 minutes, but her low effort took a deflection and then rebounded off the right post for a corner.
The resulting corner saw Gesa Marashi line up an effort from range, and her strike clipped the top of the crossbar as it sailed towards Eve Annets' goal.
Fortune would swing the other way ten minutes later, as London City took the lead through Parris.
Eva Jakobsson made a deep foray into the Palace half and her cross was deflected into the path of Parris, who took a touch and fired into the net.
It proved to be a frantic end to the game in South London, with both sides going very close.
The crossbar would deny the visitors a second time on 84 minutes, before a calamitious back pass almost gave the Eagles an equaliser five minutes later.
It appeared to the Palace faithful that the ball had crossed the line, but the referee thought otherwise as play was able to continue.
The London City net rippled on the third minute of extra-time after a dangerous corner from Weerden, but the referee deemed there to be a foul in the box, and so Palace were again denied.
The 2-1 result at the VBS leaves Palace in third place in Group D. This comes after Leicester City's 5-1 win over Ipswich in the group's other match.
Next up for the Eagles is an away trip to Durham, and you can secure your spot by clicking the button below!
