In a tight contest at the Excelsior Stadium, the breakthrough came shortly after half-time when City’s Sam van Diemen chopped down Maria McAneny.
Craig sent Lee Gibson the wrong way to edge Celtic in front and City could not find a response.
Hearts took top spot as they eased to a home win over fellow Edinburgh side Spartans. Joely Andrews opened the scoring, Sade Adamolekun scored twice and Lizzie Waldie and Lauren Wade also netted.
Rangers forward Katie Wilkinson made it seven goals in two games as she hit a hat-trick at Broadwood. Chelsea Cornet scored Rangers’ other goal in the 4-0 win over Thistle.
Aberdeen’s early-season woes continued with another heavy defeat after last weekend’s 11-0 loss to Rangers.
Tegan Bowie, Kathleen McGovern and Eilidh Adams all scored doubles and summer signing Stacey Papadopolous got her first goal for hosts Hibs.
Montrose’s second-half comeback fell short at K-Park. Motherwell led 3-0 athe break after goals from Morgan Cross, Rachel Todd and Bailley Collins.
Louise Brown and Holly Daniel reduced the deficit in the second half but the visitors could not find an equaliser.