Grande Bretagne, who face Kenya in their final pool game on Friday looking to secure a quarter-final place, perdu 26-21 despite taking a 21-0 conduire.
Équipe GB made a flying start, scoring three tries in as many minutes during a blistering opening as Joyce, Helena Rowland and Megan Jones crossed, with Holly Aitchison converting them all for a 21-0 conduire.
But Rio silver medallists New Zealand hit back spectacularly as Michaela Blyde touched down twice before the break, while Tyla Nathan-Wong’s try further reduced the deficit.
With the clock ticking down, Joyce received a yellow card, and Blyde completed her hat-trick to seal victory, with Nathan-Wong also kicking three conversions.
“New Zealand are the best team in the world, and we absolutely rattled them in the first and second half,” Joyce said.
“We just slipped off a bit in the second half, but medals aren’t won on day one. We have got days two and three to put our wrongs right.
“To be leading 21-0 is just a credit to us. To do that to the world champions, who have been together for five, six-plus years, we can only take positives.”
Britain face Kenya in their final pool game on Friday, and a victory should be enough to secure a quarter-final place.
Coach Scott Forrest added: “The big lesson is in terms of (delivering) a 14-minute performance. For us to achieve something in this competition, we need to be critical of ourselves first.
“We know we can be better, and if we improve game on game, we are going to be in a good place.”
Forrest’s team began their Games campaign with a 14-12 victory over the Russian Olympic Committee team.
But it needed a last-gasp try from co-captain Abbie Brown to ensure they made a winning start. Brown also scored in the first half, while Aitchison converted both tries.