For the third campaign in a row, Villa's ambitions have been dented by poor early season form.
This draw means Natalia Arroyo's side have failed to win their opening three WSL games for the third successive year.
But they have an excuse this season as two of those matches have been against Chelsea and Arsenal, and their resolution here gives them hope they will not be battling at the bottom for long.
They recovered well from the early mistake and the defence was solid thereafter. When punctured in the second half, ex-Arsenal keeper D'Angelo was on hand to make a fine reaction save from Katie McCabe's drive.
And they created chances - home keeper Daphne van Domselaar twice had to make fine saves from Lynn Wilms free-kicks, and Chasity Grant came close to sliding the ball home early in the second half, before Parker bundled in their late goal to spark celebrations.
Arroyo does have some issues to solve. Villa have only scored twice in four games across all competitions and remain over-reliant on Rachel Daly, who made her 100th WSL appearance here.