And the Yorkshire men had a two goal advantage following another defensive howler. Moore misjudged the long ball over the top, and Tudgay nipped in to fire past Price.
However Kenny Miller pulled one back for the Rams before Giles Barnes fired home through a crowded penalty area to force a replay.
Elsewhere, Leauge One strugglers Bristol Rovers forced a replay against Premiership side Fulham at Craven Cottage. The London outfit had to come from behind twice as first Danny Coles and then Craig Hinton had put Bristol ahead. David Healy and Danny Murphy were on target for Fulham.
Arsenal also progressed to the fourth round comfortably seeing off Championship side Burnley 2-0 after some risky moments could have seen the joint favourites slip out of the competition.
Kyle Lafferty rocked the crossbar, before Eduardo cooly put the Gunners ahead.
The win was complete when Lafferty saw red for a challenege on Gilberto and Bendtner slotted a second infront of the 3,000 travelling fans.