The home side looked to be sliding to their third defeat in four league games until Noone salvaged a draw with only eight minutes remaining.
David Marshall was by far the busier goalkeeper in a first half dominated by the visitors, Chris Martin firing wide early on before Ben Turner headed over at the other end.
Marshall reacted well to tip away a thundering, dipping volley from Paul Coutts, and Craig Forsyth's drive from the edge of the box narrowly missed the target.
Martin had the ball in the net on the half-hour only to be denied by the offside flag, and another excellent strike from Coutts was palmed away by the agile Marshall.
Cardiff finally tested Adam Legzdins after the break, and the County keeper's reflexes were up to the task as he denied Frazier Campbell at point-blank range.
Tommy Smith drilled wide as the hosts got on top, but Derby who broke the deadlock against the run of play on 75 minutes when a deflected Ben Davies shot ran kindly for Conor Sammon to flick home.
But their lead lasted only seven minutes as Legzdins misjudged the flight of Andrew Taylor's cross and Noone was on hand to nod in at the far post.
Noone, Rudy Gestede and Taylor all went close to snatching late winners, but Derby survived a barrage of pressure to clinch a battling point.