The result sees them back atop the competition table with one game left in the regular season.
Zawada was expected to miss the rest of the season because of a thigh injury he suffered in February.
The loss comes despite Man City shooting 25 more times than Real Madrid.
The deal has created a new record for Women's A-League transfer fees.
"Sometimes, for young players, the personal things are ahead of the team."
The NZ U17 international could have been a target for A-League expansion club Auckland FC.
City are alone atop the competition table, after their win over Luton Town on Sunday (NZ time).
The Welsh club has been made famous by the documentary series 'Welcome to Wrexham'.
City have put the pressure back on rivals Liverpool and Arsenal
Giancarlo Italiano has constructed the club's most successful season in his first year at the helm.
The winning effort was officially credited as an own goal in the 96th minute.
"I think it's going to be about that little edge, that small difference that no one sees," said Giancarlo Italiano.
The new system will be implemented from next season.
Atletico Madrid beat Borussia Dortmund in the day's second fixture.
Wellington sit in second place with three games remaining.
His go-ahead penalty was his 39th goal for the German club this season and 15th against Arsenal in his career.
The rivals are the last two teams to win the European club trophy.
The NZ women had beaten their rivals 4-0 three days earlier.
The Merseyside club have dropped further down the ladder.
The midfielder is hanging up her boots after a 166-game career at senior level.
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