The influential defender was sent off in the 32nd minute after he brought down Omar Bugiel when the Sutton player got on the goal side of him and Rob MIlsom scored from the spot.
The Bantams responded immediately, equalising two minutes later when striker Theo Robinson headed Elliot Watts’s free-kick into the net.
Sutton went back in front in the 75th minute following a mistake by goalkeeper Sam Hornby, who fumbled a cross from substitute Ricky Korboa and Alistair Smith scored with a close-range header.
Bradford equalised five minutes later when Lee Angol slid the ball into the net at the far post from Levi Sutton’s cross.
It was Bradford’s sixth draw in a run of seven league matches without a win, but Adams said: “I am extremely proud of the boys because it was a difficult afternoon for them after going down to 10 men.
“They showed real fighting spirit. We showed we had character in the dressing room – a team of fighters and winners. I have spoken about that before and today we had people who were willing to run and work for the team.
“The magnificent supporters stood to applaud the players off the field because they knew they were up against it after half-an-hour. They could see the energy and endeavour they put in.”
Bradford City: Hornby, Threlkeld, O’Connor, Canavan, Ridehalgh, Songo’o, Sutton, Watt, Gilliead, Robinson (Cooke 86), Angol. Unused substitutes: O’Donnell, Foulds, Kelleher, Evans, Cousin-Dawson, Lavery.
Sutton United: Bouzanis, Barden, Goodliffe, John, Wyatt, Randall (Bennett 88), Bugiel (Korboa 73), Milsom, Ajiboye (Boldewijn) 85), Wilson, Smith. Unused substitutes: Dundas, Sho-Silva, Chalupniczak.
Referee: P Wright (Merseyside).