Andy Cook’s fourth goal of the season three minutes from time saw the Bantams go second in the League Two table after four games.
Paudie O’Connor’s first-half header put the away side ahead but Oliver Hawkins scored either side of half time for the hosts to put them in front.
Charles Vernam equalised for the Bantams before Cook’s clincher sparked joyous scenes in the away end.
“That was a fantastic performance from us from start to finish,” reflected Adams.
“To come to Mansfield and have more shots on target than them with the firepower they have just showed you how well we played. We know the threat Mansfield have – they have bought big over the summer – one of the biggest spenders in the division – and we have dealt well with it.
“They are a fantastic outfit and they have a great manager in Nigel Clough. It was a great advert for League Two and having supporters back in makes it even better. The game was end-to-end with a lot of good football on show and both teams looking to get the victory.
“Our following made all the difference today and got us over the line. Andy did what he’s done throughout his career. He was the coolest man in the stadium in being able to lift it over the keeper and get the winner.”
Bradford City: O’Donnell; Cousin-Dawson, O’Connor, Canavan, Ridehalgh; Songo’o, Watt (Evans 67), Cooke (Crankshaw 83), Vernam; Gilliead, Cook. Unused substitutes: Hornby, Foulds, Kelleher, Scales, Lavery.
Mansfield Town: Bishop; Hewitt, Rawson, Perch, McLaughlin; Maris (Stirk 50), Clarke (Sinclair 88), Quinn, Oates (Lapslie 72); Johnson, Hawkins. Unused substitutes: Shelvey, Burke, Gordon, Bowery.
Referee: S Oldham (Lancashire).