Dean Windass struck 10 minutes from time to rescue a draw for Bradford as Swansea lost top spot in League One.
Windass salvaged a point for the Bantams
The striker was sharpest to head home from the back post, after team-mate Tom Penford had managed to nod a long ball back across the Swansea goal.
Steve Claridge nearly claimed all three points for Bradford, but his injury time shot was saved by Willie Gueret.
The Swans had taken the lead a minute before half-time when Gary Monk struck home Andy Robinson's inswinging corner.
Bradford: Ricketts, Holloway, Wetherall, Bower, Emanuel, Muirhead (Stewart 69), Windass, Bridge-Wilkinson, Petta (Penford 59), Brown, Claridge.
Subs Not Used: Howarth, Kearney, Wright.
Goals: Windass 80.
Swansea: Gueret, Tate, Austin, Monk, Ricketts, Britton (Forbes 83), Martinez, Robinson, Williams (McLeod 83), Knight, Akinfenwa.
Subs Not Used: Thorpe, Connor, Watt.
Goals: Monk 44.
Ref: N Miller (Durham).