Hantuchova saw her world ranking plummet to 62 in 2014, losing in the first round of 12 of her 24 tournaments, though she had wrist injury issues to contend with.
She arrived in New Zealand on the back of four straight first round defeats but she looked in superb form against the Italian clay court specialist Errani winning 6-3 6-2 in 75 minutes.
Her victory over an error-prone Errani, the world No 14, was her first win over a player in the top-100 since last July.
Errani was not the only seed to fall on the opening day of the tournament with eighth seed Mona Barthel hammered 6-2 6-1 by?? Croatia’s Ana Konjuh, while 2010 champion Yanina Wickmayer of Belgium was beaten by 18-year-old American Taylor Townshend.
Sixth seed Sloane Stephens advanced with a 6-3 6-1 victory over Silvia Soler-Espinosa.
Top seed Caroline Wozniacki and last year’s beaten finalist Venus Williams will play their first round matches on Tuesday.