It took around 10 minutes for the match to settle down, and when it did, Ardhe Nuhiu saw his right-footed shot blocked by the home defence.
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Kieran Lee then had a similar effort as Wednesday began to see more of the ball.
The Owls continued to have the better of the attacking play and Caolan Lavery had a chance to give his team the lead, but he slipped around 15 yards from goal and Rochdale cleared.
With the second half just five minutes old, the away side broke the deadlock thanks to Joe Mattock's close-range header.
They doubled their lead moments later as Oguchi Onyewu stabbed the ball home from just a few yards out. However, the game was then turned on its head.
Rose drove home a fierce long-range shot to halve the deficit, before Mattock was sent off for a second bookable offence.
Dale pushed and George Donnelly and Rose had shots saved by Martinez in the Wednesday goal as the away side held on.