But the cat-like, 1.93m Safin was not done with.
Breaking the Swede in the first game of the second set was enough to get him through 6-4 and into a deciding third set. But there remained the feeling that perhaps his heart was not completely in it.
At 3-4 and 15-15 in the third, games going with serve, Bjorkman called for the trainer to have a blister retaped.
That appeared to upset the big Russian's concentration, although he later shrugged off such suggestions.
He needed his seventh ace to save a break-point. That was only a temporary reprieve, however, as Bjorkman won three of the next four points for a 5-3 lead.
Tossing in his 10th ace, Bjorkman served the game out to love to book his place in the quarter-finals.
Safin fell well short in his bid to join John Alexander (1983), Miroslav Mecir (1987), Magnus Gufstafsson (1994) and Marcelo Rios (1998) as top seeds to win in Auckland in the past two decades.
"It was a bit difficult to start the match," said Safin, who will celebrate his 22nd birthday on January 27, the last day of the Australian Open, where he is seeded 10th. "I try hard to concentrate. I lost the first set basically because of that.
"For the second match of the year I felt okay. I was more worried to find my game as I have not played outdoors for a long time."
It was Safin's first loss in five matches with Bjorkman. He at least got something from playing two tough three-setters against Michael Chang and Bjorkman.
"I have a few things to improve before Australia but I'm satisfied with the way I'm playing," Safin said. So Safin's second visit to Stanley St ended in the same way as the first, knocked out in the second round.
Will he be back for a third? "Definitely. I would love to come back. I feel sorry for the people. I tried. I will come back to try again next year."
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