Then, teenage substitute Hakeeb Adelakun grabbed a deserved point for the visitors with an angled right-foot shot that sneaked into the net just inside the far post.
Bradford went in front after 32 minutes with defender Rory McArdle’s left-foot shot from the edge of the area after Scunthorpe failed to clear Billy Clarke’s cross.
However, Scunthorpe, who have lost only once in 12 matches, were a constant threat and twice had the ball in the net through defender Miguel Llera in the 22nd minute and striker Paddy Madden in the 70th minute only to have the efforts disallowed, once for a foul, the other for offside.
Pickford, on loan from Sunderland, made super saves to deny Richard Brindley, Luke Williams, Gary McSheffrey and Madden before being beaten by Adelakun’s last-gasp equaliser for the Iron.
Bradford are unbeaten in seven matches and a point outside the play-off zone. Parkinson claimed: “The momentum is still there and although it was frustrating for us not to hold on to our lead, you cannot take it away from Scunthorpe. They are on a terrific run and played really well.
“We gave everything we had, but we didn’t have enough quality in the second half to kill the game.
“We got pinned in our own half and didn’t play well enough to get out.”
Bradford City: Pickford, Darby, McArdle, Meredith, Morais, Liddle, Knott (Halliday 76), Yeates, Stead (Zoko 89), Clarke (Hanson 82). Unused substitutes: Williams, Sheehan, Kennedy, Routis.
Scunthorpe United: Slocombe, Brindley, Boyce, Llera, M Williams, O’Neil, Bishop, McSheffrey (Adelakun 82), L Williams, Madden, Osbourne (Taylor 89). Unused substitutes: Olejnik, McAllister, Canavan, Hawkridge, Davey.
Referee: P Gibbs (West Midlands)
Man of the match: Jordan Pickford.