Burling and Tuke placed 2nd in what was the opening race of the finals series, then suffered a mid-fleet finish with a 15th in the next. Adding a 9th after that, the Kiwis then took a race win to end the day on a high note.
"Today was some of the shiftiest racing we have done in a long time; huge gains and losses," Burling said. "We were pleased to come away with a solid enough day, all things considered."
Meanwhile Alexandra Maloney and Molly Meech (Tauranga) will go into the final day of racing 8th overall in the women's 49erFX Championship. Like their male team mates their results were mixed and ended on a high - 8, 19, 7, 1.
Denmark's Ida Marie Nielsen and Marie Olsen are leading from Martine Grael and Kahena Kunze of Brazil.
The schedule for tomorrow is to sail three more finals races for the gold fleets before the top ten in both the 49er and 49erFX duke it out in the medal races.