Three seeded players - No 1 Angeles Montolio, No 4 Conchita Martinez and No 6 and defending champion Meilen Tu - crashed out.
Away from the glare of centre court, eighth seed Mariana Diaz-Olivia also departed, beaten in straight sets by Silvija Talaja.
Of the eight players left in the top half of the draw, American Amy Frazier, the No 7, is the only seeded survivor.
She meets Kournikova in the second match on centre court, in what promises to be the best of today's matches. Again, organisers have held back 40 tickets and three courtside boxes for the public.
Kournikova began tentatively against Black.
With a large slice of the 3400 crowd - the biggest to watch a women's match in New Zealand - behind her, she struggled to hold serve in the opening game.
Black levelled at 1-1 then broke the Russian to love, eventually taking a 4-1 lead.
While some of the tennis was first-day-of-the-year stuff with too many unforced errors, there were glimpses of class as Kournikova fought back to 5-6 and then broke Black to force a tiebreaker.
Black took the initiative, sweeping to 4-1.
But Kournikova was not done, even if Black, at 6-5, held set point. Kournikova won two points on serve for 7-6 and then the set when Black's cross-court backhand flew wide.
The second set took only 30 minutes as Black dropped her serve in the first and seventh games.
"She got her confidence and became aggressive after the first couple of games," Black said. "It was tough to keep up once she got into her mode."
Asked whether playing in such a cauldron was a problem, Black said: "I had to concentrate on my game and block everything else out."
Kournikova was not too fazed by the on-court heat. "I've played in 43 degrees in South Africa," she said.
"I was a little bit excited about my first match of the year. I'm looking forward to my next. It was important to win the tiebreak. I would be pretty sad, I guess, if I had lost from there."
Kournikova said she fed off the crowd's enthusiasm.
Martinez showed only glimpses of the form which won her Wimbledon in 1994, going down 6-7 (5-7), 3-6 to unseeded American Kristina Brandi.
Broken in the first game, Martinez got back to 3-3 and eventually 6-6 without ever really showing her best.
She rallied after being down 0-3 in the second set, but after reaching 3-3 her run ended and Brandi coasted through to the second round.
Top seed Montolio never raised a yelp in going down 3-6, 1-6 in an hour to Russian Alina Jidkova.
"I was a little surprised at the way she fell apart," said unseeded Jidkova, who earned the right to play here with her win in a $US50,000 tournament in Pittsburg in November.
"She [Montolio] is usually a fighter, but she did not show much today. I was nervous playing my first match of the year against the top seed."
For Spaniard Montolio, the 23rd ranked player on the WTA list, her first tournament as a top seed was one she will be happy to forget.
"I did not find a way to play my way into the match," Montolio said. "I have to go and practice to play better."
Montolio had a nightmare journey to Auckland from Spain, arriving on Saturday after two extra days of travelling caused by flight changes. Her luggage did not get here with her. But she did not blame that for her downfall to Jidkova, ranked 107 in the world.
Last night, second seed Henrieta Nagyova, of Slovakia, beat doubles partner Kveta Hrdlickova, of the Czech Republic, 7-5, 6-2.
New Zealand's participation ended when Shelley Stephens and partner Joana Cortez lost a drawn-out doubles to Tu and Emmanuelle Gagliardi 4-6, 5-7.
Earlier, Stephens bowed out in the singles, 2-6, 1-6, to qualifier Barbara Schwartz.
Today's schedule. -
Centre court (from 11 am): Barbara Schwartz v Anne Kremer, Anna Kournikova v Amy Frazier, Tatiana Poutchek v Henrieta Nagyova, Alina Jidkova v Anna Smashnova, Emmanuelle Gagliardi/Melien Tu v Maria Jose Martinez/Anabel Garrigues.
Court four (from 11 am): Tatiana Panova v Jennifer Hopkins, Anabel Mendina Garrigues v Selima Sfar, Silvija Talaja v Maja Matevzic, Kim Grant/Abigail Spears v Hrdlickova/Nagyova.
Court six (from noon): Kristina Brandi v Gagliardi, Maria Emillia Salerni/Patricia Tarabini or Mariana Diaz-Olivia/Julie Pullin v Panova/Poutchek.
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