James Hanson climbed off the bench to secure Bradford a 1-1 draw against Dagenham at Valley Parade in League Two.
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The Bantams, beaten 5-0 at Wembley on Sunday, looked to be heading for defeat against the Daggers, who this week saw long-serving boss John Still depart for Luton.
Interim manager Wayne Burnett was eyeing three points courtesy of Luke Howell's 69th-minute strike but the Bantams hit back with four minutes to play.
The hosts included just five of the players who started against the Swans and they could have fallen behind early in the second half had striker Sam Williams not fired his penalty wide following Kyel Reid's foul on Luke Wilkinson.
Williams went some way to redeeming himself when he played a part in Howell's opener, with the midfielder providing a clinical finish from the edge of the box.
But Bradford kept at it and levelled when Hanson, on as a substitute in the 66th minute, supplied the finishing touch from a Zavon Hines cross.