After a 1-0 loss to hosts Sweden and a penalty shootout defeat to Austria, Sharon Boyle's side ended a rewarding trip with a well-deserved win in Lysekil.
Ziu's goal came from a short corner with the midfielder heading home at the back post, to guarantee the three points
Head Coach Sharon Boyle said the three games have proven very beneficial for the team's development, before the move on to Under-17 level.
"You couldn't have asked for better opposition. I'm proud of how everyone applied themselves this week in Sweden. It's a very strong group that will now move onto the Under-17s.
"The girls had to dig deep today. You could see their relief when Jessica scored. All their hard work this week paid off.
"Only Muireann Devaney and Aoibheann Clancy will be with the Under-16s next year. The rest will move onto the Under-17s. They now know what's expected of them when they move up an age grade."
Republic of Ireland: Courtney Maguire; Eabha O'Mahony, Ellie Ferguson, Mia Dodd, Zara Foley; Jessica Ziu, Aoibheann Clancy, Muireann Devaney; Shauna Carroll, Lauren Egbuloniu, Sophie Liston
Substitutes used: Kayla Brady, Hana Ueno, Nadine Clare, Emily Whelan, Blessing Kingsley, Bobbi Downer