A brace of goals from Graham Kavanagh gave Cardiff their second victory of the week to keep their promotion hopes alive.
Kavanagh struck in the 36th minute when he fired home from a Peter Thorne knock-on, and his second goal came from the penalty spot on the hour-mark after Leyton Maxwell had been bundled over in the area.
Conditions made good football difficult and it was only after the second goal that the Bluebirds took control.
Lennie Lawrence kept faith with the line-up that started against Bury in midweek but Mark Bonner, who passed a late fitness test, had to give way to Maxwell eight minutes into the second half.
Kavanagh's double took his goals tally to 15 for the season and City will miss him when he sits out the next two matches due to suspension.
