Stephen Warnock’s late cross from the left looked harmless enough, but after Rochdale goalkeeper Josh Lillis initially gathered the ball, he then inexplicably dropped it at the feet of Wyke, who gleefully tapped into an unguarded net from four yards.
It was fortunate because Rochdale had been the better side for the most part as they continued their gutsy battle to try to stave off the threat of relegation.
Bantams’ manager Simon Grayson said: “We just needed a bit more quality in the first half in particular.
“We needed to get the ball down and play a bit more, though I can’t fault the lads for the effort they put in.
“We’ve got to keep battling on during these final four games now, and I’m seeing a good attitude among the players right now.
“The play-offs might not happen now this season, but I’m seeing positive steps.
“They’re small steps, but it’s all about thinking towards next season.”
The Bantams looked a little edgy throughout the first period at the Crown Oil Arena and unsurprisingly found themselves behind at the interval.
Left-sided Matty Done grabbed the goal for the hosts, latching on to Joe Thompson’s cross before lashing the ball across goalkeeper Colin Doyle and into the far corner of the net.
Earlier Doyle had been forced into a smart close-range stop from Thompson, and at the other end Matthew Kilgallon headed narrowly over the top as he charged in to meet Matty Lund’s cross.
Seconds before the interval Rochdale almost went two clear as Bradden Inman hit the outside of a post from the tightest of angles.
The Bantams were better in the second period, and almost levelled when Wyke volleyed over from eight yards after meeting Tony McMahon’s cross.
It was left to Wyke to rescue a point, however, courtesy of Lillis’s awful mistake.
The Bantams host MK Dons tomorrow night.
Rochdale: Lillis, McGahey, McNulty, Delaney, Rafferty, Camps, Rathbone (Ntlhe, 51), Thompson (Humphrys, 74), Done, Andrew, Inman (Gillam, 85). Unused substitutes: Wiseman, Moore, Morley, Dobre.
Bradford City: Doyle, Lund (McCartan, 90), Kilgallon, Knight-Percival, Warnock, Gilliead, Dieng, Vincelot (Poleon, 77), McMahon, Wyke, Brunker (Law, 54). Unused substitutes: Chicksen, Raeder, Devine, Patrick.
Referee: O Yates.