Gareth Taylor's side remain perfect in the Champions League but were made to work hard for the three points against the Swedes.
Manchester City struggled to impress in a hard-fought 2-0 win over Hammarby but made it nine points from nine thanks to second-half goals from Laura Blindkilde Brown and Aoba Fujino.
The hosts made hard work of a dire first half but came flying out of the blocks after the break and scored within minutes of the restart. Bunny Shaw fired in a low ball from the left for Blindkilde Brown to side-foot home for the opener.
City looked set to run away with the game after going ahead but once again toiled. Shaw did have the ball in the back of the net only to see her effort correctly ruled out for offside. Hammarby then created a scare when Thea Sorbo's powerful effort had to be tipped over the crossbar by goalkeeper Ayaka Yamashita.
Instead it was left to Fujino to finish off the visitors with 10 minutes to go. Leila Ouahabi sent in a cross from the left for a stooping Fujino to head home and complete the victory.
GOAL rates Manchester City's players from the Joie Stadium…
AFPGoalkeeper & Defence
Ayaka Yamashita (7/10):
Was a bystander for most of the much of the match but pulled off a great stop from Sorbo in the second half.
Kerstin Casparij (6/10):
Decent outing from the full-back.
Alanna Kennedy (7/10):
Used the ball well and was not really tested defensively.
Alex Greenwood (7/10):
Good delivery from set-pieces and untroubled at the back.
Leila Ouahabi (7/10):
Put in some dangerous balls, including a great cross for Fujino to score City's second.
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Laura Blindkilde Brown (7/10):
Was in the right place to bag home the opener with a neat finish on her Champions League debut.
Yui Hasegawa (6/10):
An energetic display as usual.
Jess Park (6/10):
Not at her very best. Struggled to link the play.
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Mary Fowler (7/10):
City's best player by some distance. Involved in all their most dangerous play.
Bunny Shaw (6/10):
Grabbed an assist and had a few bright moment but overall a frustrating night for the striker.
Aoba Fujino (6/10):
Had missed a host of chances before heading home City's second late on.
AFPSubs & Manager
Chloe Kelly (N/A):
Came on late to help see the game out.
Jill Roord (N/A):
Another late sub, with the game already won.
Laura Coombs (N/A):
Stoppage-time sub.
Gracie Prior (N/A):
Stoppage-time sub.
Lily Taylor (N/A):
Only given a few minutes.
Gareth Taylor (6/10):
May have had one eye on the weekend's clash with Chelsea but saw his side just about do enough to win.