They finished strongly, shutting out the hosts 29-14 to take the bronze medal, equalling their Cape Town placing, despite resting several players, including captain Scott Curry.
DJ Forbes filled the breach admirably in his record-extending 83rd World Series tournament, while Ware, who usurped Sione Molia for a starting berth on the wing, crossed for his fourth try in Sydney, leading all New Zealand try-scorers. The team highlight was Trael Joass' first try for his country, finishing a movement set up by Rocky Khan.
In the Cup final, South Africa beat England, also 29-14, to record their third title in four outings for 2016-17, proving they are the world's best sevens team on form.
Scott Waldrom's charges will have a month to plan, recharge and rethink before the March 3-5 Las Vegas tournament, the fifth leg of the World Series. They are now 11 months without a Cup victory, but it may not be far away.
There were some topsy-turvy results over the two days in front of good crowds. Wales lowering Fiji was the biggest upset, but they did not kick on. Scotland, Cup semifinalists in Wellington and Cape Town, could not even finish in the top 14. New Zealand edged them 14-7 in the final match of day one.
• The Black Ferns Sevens also had to settle for third after defeating hosts Australia 19-0 for the bronze medal, but were off colour for much of the event, despite some silky skills from Kat Whata-Simpkins.
However, they have a four-point lead over Australia at the top of the Women's World Series standings. Canada were the unexpected Cup victors, defeating the United States, who had knocked out New Zealand in the semifinals.