A largely uneventful Yorkshire derby was settled in the 73rd minute when City were caught on the break with Leeds United loan winger Wilks unleashing a low shot which underneath the body of home keeper Richard O'Donnell before nestling in the net.
It was big blow for Bradford, who failed to the crown the weekk which saw manager Gary Bowyer sign a two-year contract with the club with a cherished victory to boost their fight against the drop.
Rovers, meanwhile, secured their third victory on the trot to firmly consolidate their place in the League One play-offs.
The early offerings saw City set off with intent before Rovers started to show signs of getting their passing game together - only for the game to descend into a scrappy affair for the final 15 minutes of the first period.
The closest to an opener arrived on nine minutes when a superb glancing header from Eoin Doyle struck the post after a pinpoint left-wing centre from Billy Clarke, recalled alongside Nathaniel Knight-Percival and Adam Chicksen.
City's other dangeroous moment arrived earlier when a clever short-corner routine ended with Jacob Butterfield's goalbound low shot diverted away from goal by the alert Tom Anderson, brought into the side for Paul Downing.
Rovers' threatened on a couple of occasions, with Ali Crawford - busy in the first half - firing just wide and Kieran Sadlier heading just off target.
After starting off well, City replicated that feat in the second half with David Ball firing a low shot just off target after an enterprising run and former Rovers loanee Jermaine Anderson just failing to get a telling connection in front of goal after fine work by Doyle.
Most of the pressure came from the hosts, but a breakthrough stubbornly refused to arrive - and the sting arrived when Rovers broke the deadlock on the counter attack.
The ball found its way to Wilks and with City stretched, the loan winger drove at the home rearguard before firing home a rasping low drive which went under O'Donnell.
The closest that the hosts came to a leveller saw Butterfield fire a daisycutter just wide.
Bradford City: O'Donnell; Caddis, P O'Connor, Knight-Percival, Chicksen; J Anderson (Payne 76), Butterfield, O'Brien; Ball (Akpan 86), Clarke (Scannell 76); Doyle. Substitutes unused: Wilson, A O'Connor, Scannell, Devine, Wright.
Doncaster Rovers: Marosi; Blair, T Anderson, Butler, Andrew, Crawford, Rowe; Wilks (Downing 87), Coppinger (Beestin 74), Sadlier (May 57); Marquis. Substitutes unused: Jones, Smith, Hasani, Lewis.
Referee: D Whitestone (Northants).