At the same tournament in Tasmania, Sitak easily beat Uzbekistan's Temur Ismalov 6-1 6-2 in the first round of qualifying before going down to Australian Adam Feeney 5-7 0-6 in the second round.
Venus and King-Turner were unable to make Burnie qualifying after reaching the second round of the doubles at a Challenger tournament in Honolulu. The pair are back in Auckland training before heading to Tauranga this weekend with the rest of the squad.
Venus, New Zealand's No1-ranked player, has done well in Challenger events over the past couple of years, while Sitak won through to the final round of qualifying at last month's Heineken Open.
Statham won the recent New Zealand Championship title and has a great record in Davis Cup for his nation, with an 18-4 win-loss record in singles.
King-Turner, 27, returns to the side for the first time since 2010 after being sidelined for most of 2011 with an ankle injury. He combined with Venus to make the semifinals of the Heineken Open doubles.
"It's a good, solid team with some firepower and plenty of Davis Cup experience," Vos said.
"Mike has some big weapons and has shown he can match it with the best on the day.
"Rubin has been a passionate and reliable performer for New Zealand with a great Davis Cup record.
"Artem is a true professional with great work ethic and has added a lot of depth and team spirit to our team.
"Having Dan back in the team for this tie gives us more options and he formed a great partnership with Mike in doubles."
If New Zealand win, they'll play India in April for the right to advance to the world group playoffs. A loss means they would play again in September against an unknown opponent and defeat in that tie would send the country back down into group two.
Vos said Uzbekistan, who beat New Zealand 3-2 a year ago on clay in Namangan, would provide a stern test for the Kiwis.
"Uzbekistan are tough and any side that has a guy like Istomin offers a great challenge for us. He is obviously a quality player but in Davis Cup, the largest annual teams event in sport, it is about a team and a nation, which makes it different than any other tournament.
"We are going to be well prepared for this home tie and work together as a team. Our depth gives us playing options, which can be important."