Sweden were given a scare by South Africa before winning 2-1 at the death at the Women's World Cup on Sunday while 2019 finalists the Netherlands also began their campaign with victory by a single goal.
France, who have never lifted the World Cup but are among the favourites in Australia and New Zealand, played a goalless draw against Jamaica in Sydney in the last match of the day.
The third-ranked Swedes fought back from a goal down and conjured up the winner in the 90th minute through Arsenal defender Amanda Ilestedt, much to the relief of their fans in miserably wet conditions in Wellington.
A goal early in the second half by Hildah Magaia -- in which she suffered a match-ending injury -- had given South Africa hope of an upset in front of 18,317 spectators.
But that was soon cancelled out by Barcelona star Fridolina Rolfo before Ilestedt's late intervention, heading home from close range for a hard-fought victory.
It denied the African champions a first point ever at the World Cup.
The Dutch, losers 2-0 to the United States in the final four years ago, had less trouble against debutants Portugal in the New Zealand city of Dunedin.
Defender Stefanie van der Gragt put them on their way after 13 minutes with a powerful header from a corner.
The Netherlands now face holders the United States on Thursday in a rematch of their final, with Group E supremacy at stake.
Two-times former champions Germany enter the fray on Monday when they face World Cup debutants Morocco.
Germany are among the favourites to win the tournament but their coach Martina Voss-Tecklenburg warned that women's football has never been more competitive.
Also on Monday, Brazil play Panama.
Co-hosts New Zealand return to action on Tuesday to begin the second round of group matches.