A Jordan Connerton hat-trick sent Phil Brown's side to 7 points clear at the Evo-Stik summit.
Connerton opened the scoring late in the first half, rising highest to head home Craig Carney's cross at the back-post. Radcliffe fought back and levelled the score when Yahya Saeed converted from close range but the lead lasted only minutes.
Connerton got his second from the spot after being scythed down in the box, sending the keeper the wrong way to restore City's lead at 2-1.
Late in the half he wrapped up his hat-trick after latching onto Billy Akrigg's through ball, rounding the keeper, and coolly converting from a tight angle.