Hanley replaced Morten Gamst Pedersen in Rovers' only change from Saturday's 1-1 draw at Derby and he immediately repaid the faith of caretaker boss Eric Black by opening the scoring from close range.
Michail Antonio spurned Wednesday's best chance of an opening period where Rovers were largely on top.
It was a different story after half-time with Dave Jones' side in the ascendancy.
A solo effort from Lewis Buxton was the closest they came to an equaliser merited on pressure and intent if not clear-cut chances, but Blackburn held on to give Black his first taste of victory at the fifth attempt since Steve Kean's resignation last month.
Rovers vault into the play-off places on goal difference, while Wednesday - winless in the league since August - slip to second bottom by the same means.
Jay Bothroyd failed to recover from illness and was replaced by Gary Madine in the Wednesday attack, while skipper Martin Taylor and winger Jermaine Johnson returned at the expense of Anthony Gardner and Chris O'Grady.
Goalkeeper Chris Kirkland started for the visitors in the first match since he was attacked on the field by Leeds fan Aaron Crawley in last week's Yorkshire derby.
Madine might have given Wednesday a second-minute lead when he rose unchallenged to head over from Paul Corry's corner, but Jones' men were soon behind.
David Dunn shrugged off the attentions of Wednesday's Everton loanee Ross Barkley, bustled to the byline inside the area and his cutback left Hanley - still up field from an earlier set piece - with a simple finish.
Having jettisoned his hitherto preferred three centre-backs approach, Black's Rovers controlled large sections of the opening exchanges with their 4-2-3-1 formation, but Wednesday came close to levelling either side of the half hour.
First Miguel Llera struck a 25-yard free-kick narrowly past the post with Paul Robinson beaten, before Antonio got goal side of Bradley Orr and wastefully shot wide.
Dunn limped out of the action after 34 minutes and replacement Ruben Rochina almost had an instant impact, forcing Kirkland into a sharp save from his rasping 30 yarder.
As at the start of the first period, Wednesday were presented with an opportunity from a Corry set piece shortly after the restart - Llera heading off target on the occasion.
The visitors remained on the front foot this time but Rochina almost punished them on the break in the 57th minute, Kirkland saving superbly with his feet after the shot deflected off Daniel Jones.
Fellow full-back Buxton nearly brought Wednesday level in fine style after the hour, cutting into the box inside Dickson Etuhu and thumping past the far post at the end of a surging run.
Wednesday continued to press but Blackburn substitute Pedersen almost gave his side further cheer when Llera hacked the Norwegian's free-kick off the goalline.
As gaps continued to open up in the visitors defence, the lively Rochina had Kirkland at full-stretch three minutes from time with a rising drive.
Source: PA
Source: PA