Carter told the new champion he "was cheering for Venus [Williams] to get to the third set [and] after that I started cheering for you".
Ivanovic was happy to receive the jersey, and quipped "It is adidas too, so I can wear it!"
Aside from her strong form, the Serbian has made the most of her Auckland visit, taking a helicopter ride over the Hauraki Gulf and visiting Piha and the Waitakeres. She plans to see some "more beautiful beaches" today, before a late flight out tonight to Australia.
Final opponent Williams has been less a tennis tourist over the past week but did, after a bit of searching, track down a karaoke bar to relax one night. It is a hobby of Williams, one she shares with her famous sibling.
"I used to have a go-to song - Call Me, by Blondie," Williams said. " Now I always try to sing new songs. I sing a lot of 80s, a lot of classic rock. Serena sings today's pop hits - and also The Little Mermaid - so that is how we differ."
Over the past week in Auckland, Williams has kept a close eye on the form of the Miami Dolphins, the NFL team of which she is a part owner, along with Serena.
"I really enjoy the games - maybe too much," laughed Williams. "But we had an extremely tough loss this week so we just missed out on the play-offs. We will get there though."