Kosovare Asllani and Carli Lloyd were on target for Sweden and the United States respectively, to ensure both nations made a winning start in France.
The second round of fixtures begin on Wednesday – day six – though no City players will be in action.
Former City midfielder, Lloyd, who won the 2016/17 FA Cup with Nick Cushing’s side, was introduced just before the hour mark as the United States recorded the biggest victory in Women’s World Cup history.
The 36-year-old became the second oldest player to score at the tournament with a close-range finish, which rounded off the 13-0 victory over Thailand.
It was Lloyd’s 275th international cap, and she now sits fourth on the all-time list for the US.
Elsewhere in Group F, Asllani crashed home the opener as Sweden emerged as 2-0 victors over Chile.
It was a poacher’s finish from the 2016 FA WSL title winner, who reacted quickest to a loose ball to fire home her first World Cup goal.
Betsy Hassett, who won the 2014 Continental Cup with City, was also in action on Tuesday, but her New Zealand side fell to a 1-0 defeat to the Netherlands.
Off the pitch, Jill Scott was playing her part to inspire the next generation.
It was the midfielder’s turn to appear in England’s Lionesses Daily show alongside Karen Carney, where the pair surprised two young fans on Facetime.
Wednesday’s action kicks off at 2pm (BST) when Nigeria and South Korea will face off in a bid to get points on the board in Group A, before France and Norway will try to steal a march on the other and go top of the group.
It’s a similar story in the final game of the day, which pits Germany and Spain against each other in Group B.