Castleford’s loss at Salford City Reds means that the relegation battle will go down to the wire as they face off with the Wildcats at Belle Vue on Saturday night – the losing side facing the drop to LHF National League One.
The hosts had opened the scoring through Michael Withers but Wakefield overcame that early hurdle; tries from Semi Tadulala, Colum Halpenny and Ned Catic along with four goals from Jamie Rooney opening up a 20-6 advantage.
Bradford pulled a try back – Michael Withers again the scorer – but the Wildcats held out to secure the vital two points.
Wakefield boss John Kear said that he was satisfied with his side’s efforts, but urged caution ahead of the crucial Castleford clash.
Kear said: "There's a feeling of satisfaction, which comes from the response of a group of players who are working really hard.
"And through that hard work, they've given themselves an opportunity and they're taking the opportunity.
"It was a heroic effort but we need to keep our feet on the ground."
Bradford coach Steve McNamara admitted that the Bulls had dosapointed, but paid tribute to Wakefield.
"All credit to Wakefield, who were very enthusiastic and played really well” said McNamara.
"The sin-binnings illustrated the way we played. It was probably the least smart game we have played. We were very dumb in a lot of the things we did. A lot of frustration built up and it showed."