Coetzer: Too good for Kournikova
It was the Russian's fifth successive first-round defeat.
Having double-faulted 25 times in a first-round loss to Anne Kremer last week in Filderstadt, Kournikova continued to struggle with her serve and gifted Coetzer an early break.
The South African then raced through the first set in just 23 minutes.
Quick exit
Kournikova opened the second set with a break but then squandered the advantage, double-faulting twice to allow Coetzer to break back on her way to a 4-1 lead.
On the verge of another quick exit, Kournikova suddenly discovered her form.
Playing with surprising confidence, she attacked the net with authority, while her groundstrokes began to find line as she took the next five games to level the match.
The contest remained tight in the third set, but Coetzer collected the decisive break to go up 5-3.
She then held serve to book her place in the second round and extend Kournikova's winless run.
Greatest win
Fellow Russian Elena Dementieva, seeded seven, lost 6-2 6-4 to the unseeded Swiss Marie-Gaiane Mikaelian.
The 17-year-old Mikaelian, who came through the qualifiers, took the contest on her fifth match point.
"It's like a dream," said a delighted Mikaelian. "I can't believe that I've beaten one of the best players in the world.
"It's by far my greatest win."
In other first round action, sixth-seeded American Meghann Shaughnessy lost 6-3 6-4 to Slovakian qualifier Daniela Hantuchova.
Fellow American Lisa Raymond beat compatriot Alexandra Stevenson 7-6 (7/4) 6-3.