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The world number 71 came back from a set down to beat Japan's Ayumi Morita 4-6, 6-0, 7-5 in a match that lasted almost two hours.
It was just the second time Erakovic has beaten Morita in eight meetings, the only other victory coming when the Japanese player retired during their only other clash on grass.
Erakovic dominated the winners count by 40-17 but was let down by unforced errors and an inconsistent first serve throughout the match. She did manage send down 12 aces in the victory over the world number 50.
It is the third straight year Erakovic has made the second round but that is where her tournament has ended on the last two occasions.
The New Zealander will face 24th seed Shuai Peng of China in the second round. The duo have met just once before, also on grass, when Peng won a qualifying match at Birmingham in 2011 6-4, 4-6, 6-3.
Erakovic's best run at Wimbledon was in 2008 when she reached the third round.