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, face 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.
Also in Group G, Italy face Argentina on Monday.
Sweden coach Peter Gerhardsson said "nerves and tension" were behind a shaky start to their World Cup campaign.
"It's OK to be nervous but you need to have the courage to still make that pass," Gerhardsson said.
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.
Sunday's match in Dunedin, played in front of a crowd of nearly 12,000, saw the Dutch have more of the ball but Portugal threatening on the break.
Portugal's first shot of the game finally arrived in the last 10 minutes but the Dutch were ultimately fairly comfortable winners.
Evacuated
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.
"All the games are tight, women's football teams have come ever closer," the former international player said on the eve of her team's opening match.
"All the countries coming here are not only proud to be at the World Cup but they absolutely have the quality to play here and to pose problems."
Also on Monday, Brazil play Panama.
Co-hosts New Zealand return to action on Tuesday to begin the second round of group matches.
The New Zealand team had to be evacuated on Saturday after a fire at their hotel in Auckland.
Defender CJ Bott called it "not ideal" and "not a situation anyone wants to be in".
"We went down the fire exits," she said.
"One was a bit smoky but the majority of us got down the other exit.
"We spent the rest of the evening in another location until the hotel was clear and everything was safe to go back."
