It ends a disappointing tournament for the New Zealand No 1, who was also knocked out of the first round of the doubles despite being seeded second with Cara Black. The pair were beaten by wildcards Sacha Jones and Abigail Guthrie in a third-set super tiebreaker on the first night of the tournament.
Erakovic played a poor match against Davis, producing too many unforced errors and not putting enough pressure on her opponent.
Davis played well, and her superior movement allowed her to dictate the match, and she will now take on the winner of tonight's match between top seed Roberta Vinci and wildcard Ana Konjuh.
Elsewhere, last year's beaten finalist and the fourth seed have both been knocked out by qualifiers on day two of the ASB Classic in Auckland this afternoon.
Yanina Wickmayer, who went down to Agnieszka Radwanska in last year's final, was out of sorts as she was dumped out by Kristyna Pliskova 7-6 (3) 6-0 on court four. Fourth seed Sorana Cirstea was the next casualty when she was beaten by another qualifier, Sharon Fichman of Canada, 6-1 6-4.
Fichman, whose highest ranking was 95 earlier this year, let out a squeal of delight on match point in one of the biggest wins of her career.
Second seed Ana Ivanovic avoided becoming another big-name casualty, overcoming a determined effort from American Alison Riske to win in straight sets.
Ivanovic broke the serve of Riske twice to win the first 7-5, before saving several set points in the second to claim the match in a tie-break.
There was a scare for the Serb - and tournament organisers - when she required the trainer for attention on her right shoulder, but she showed no ill effects upon resumption of the match.
Third seed Kirsten Flipkens was another to advance to the second round, overcoming an inconsistent serve before seeing off Puerto Rican Monica Puig 6-4 7-5 in the first game on centre court.
Flipkens, the world No 20, struggled with six double faults and a first serve success rate below 50 per cent, but her ground game was too good for an erratic Puig.
The Puerto Rican is regarded as one of the sport's rising stars but her inexperience shone through, committing an unforced error to lose a first set featuring seven breaks of serve.
The second set looked headed for a tie-break when Puig led 40-0 in the 12th game, only to play a string of wild shots and allow Flipkens to claim the match.
While the Belgian was pleased with her victory, she was equally happy with her health after struggling with knee problems since Wimbledon.
"The first match of the season is always quite difficult, but I had a good feeling on the court," she said. "For me, the most important thing was to have no pain in the knee, which was successful.
"Winning and losing wasn't didn't really matter today, but of course it's good having an extra match going into the Aussie Open."
