Fran Kirby opened her WSL account for the season but it proved to be in vain as a second-half revival saw off Dario Vidosic’s charges.
The former England international sparked hopes of a second-ever victory at the Joie Stadium with a well-taken early strike.
But new home boss Andree Jeglertz shuffled his pack after the interval and carried home the points thanks to goals from Bunny Shaw and Yui Hasegawa.
Michelle Agyemang breaks clear. 📷 Kyle Hemsley
Although Albion keeper Chaimaka Nnadozie was the busier, the visitors were well in this game from the start and they were given a boost in the 14th-minute.
The opening goal owed plenty to Michelle Agyemang’s ability and the awareness of team-mate Rachel McLauchlan.
The England international cut inside and her right-foot shot from the edge of the area was parried by City keeper Khiara Keating, the ball falling to Albion’s right-back who had moved forward in support.
Maisie Symonds hassles for the ball. 📷 Kyle Hemsley.
The Scotland defender fed Kirby and the former England international drilled a low shot into corner of the net.
Nnadozie saved well on a couple of occasions from Vivianne Miedema and Shaw before the break but the visitors’ rhythm was upset when Albion’s goalscorer was withdrawn at the interval.
And City’s pressure eventually told just before the hour when Leila Ouahabi’s left wing cross found Shaw at the back post and she headed home.
Nadine Noordam puts Gracie Prior under pressure. 📷 Kyle Hemsley.
Stung by this, Albion hit back. Substitute Kiko Seike testing Keating with an effort from an acute angle, but City took the initiative and grabbed the winner 16 minutes from time.
Sub Aoma Fujino played a neat one-two on the edge of the box before slipping the ball to Hasegawa who sidefooted beyond Nnadozie.
Albion: (4-2-3-1) Nnadozie, McLauchlan, (Auee 62) Rule, Minami, Olislagers; Symonds, (Camacho 88) Cankovic; Kirby, (Noordam 46) Rayner (Seike 63) Agyemang; Haley. (Kafaji 81).