Both sides had chances to win it, with Jordan Rhodes and Rudy Gestede both going close for Blackburn, who were indebted to their goalkeeper, Simon Eastwood, for two spectacular saves that denied Atdhe Nuhiu.
But neither did enough to deserve the win and, though the Owls remain in the relegation zone of the Sky Bet Championship, they have now kept successive clean sheets away from home.
It ended Blackburn's two-match winning run but they remain well in the mix for a place in the top six.
Blackburn boss Gary Bowyer made one change from the victory at Yeovil, which saw Gestede make his first start for the club in place of David Dunn.
Wednesday caretaker manager Stuart Gray made four changes after defeat to Bournemouth.
Wednesday made a solid start and almost took an early lead through Nuhiu's glancing header but Eastwood produced a fine save to claw the ball away low to his right.
But Rovers are in brilliant form at Ewood Park and should have taken a 12th-minute lead when Rhodes found space in the area, only to see his effort deflected into the side netting.
The forward found the net in his previous two games and was handed the opportunity to break the deadlock after Roger Johnson inexplicably headed into his path but Rhodes' placed effort 12 yards out was tipped behind by Chris Kirkland after 34 minutes.
But it was Wednesday who went closest to opening the scoring two minutes before half-time.
Stephen McPhail whipped in a glorious ball that was met powerfully by the head of Nuhiu but Eastwood produced a superb fingertip save to push over the bar.
There was an extended break in play at the end of the half after Chris Taylor collided with Glenn Loovens and was stretchered off after being fitted with a
Gestede should have marked his first Blackburn start with a goal early in the second half when he sprinted down the left and easily beat Loovens in the process but his shot was weak and allowed Kirkland to make a sprawling save before Wednesday hacked clear.
But Rovers have lost just once in their last nine at Ewood and started to show that form as the game went on. First, Josh King burst down the left, brushing off Liam Palmer but his teasing cross after 74 minutes was sliced over by the off-balance Tom Cairney.
And just a minute later, the Norwegian striker found space on the left of the area but fired straight at Kirkland who gathered at the second attempt.
But despite a frantic finish, neither side could force a winner.