Graf, though showing no sign of injury, lost concentration with the match at her mercy at 5-2 in the second set. She was pulled back to 5-5 and missed four match-points before finishing off a plucky opponent.
Coetzer, ranked No 22 in the world, never gave up and won many fine points from the back of the court but Graf, running round her backhand whenever possible, always appeared to be able to step up a gear if necessary.
Despite her back, the 26-year-old German is unbeaten this year in 27 matches and she has now beaten the diminutive Coetzer, who is only 5ft 2in, six times running over the last three years without losing a set.
After her match Graf said: "My back was fine today. Maybe I was thinking about it a little bit, like waiting for something to happen. But nothing happened and it was only my concentration that was not 100 per cent."
She said that she had fully intended to play with Martina Navratilova in the women's doubles but had pulled out so as not to aggravate her back, which she felt go a little in her first-round match with Martina Hingis.
"I've been living with my back problem for eight or nine months and sometimes it is a problem and sometimes not. Sometimes I need treatment for a few hours, sometimes a few days," she said.
Graf had hesitated until the last minute before withdrawing from the doubles. "That's why I waited so long about it, why it was such a difficult decision for me," she said. "I don't know how much I can say I'm sorry for it. I wish I wouldn't have had to do it, but there was no other way."
The only surprise in the women's singles yesterday came when Yone Kamio, of Japan, beat the experienced 16th seed, Helena Sukova of the Czech Republic, 4-6, 6-4, 6-4. Sukova was the fourth women's seed to be beaten.Reuse content