Full-back Wayne Evans was the villain with a poor clearance and Sibon pounced, cut inside and slammed the ball wide of keeper Neil Edwards from 10 yards.
Sibon went close with a 20-yard effort and could have had a hat-trick but for heroics from the Rochdale keeper who pulled off a string of saves to keep Wednesday at bay.
But Rochdale had their chances as the Sheffield defence creaked with Gareth Griffiths and Paul Connor carving out good chances.
Rochdale should have levelled matters in the 31st minute when skipper Griffiths was first to react to a Paul Simpson corner but the big centre-back headed over from eight yards.
Teenager Leon Knight, on loan from Chelsea, showed why the London club rate him so highly as he weaved past his marker to finish with a stinging shot from 10 yards smothered by the diving Edwards.
Griffiths almost snatched an equaliser on the stroke of half time connecting with a Simpson corner only to see the ball crash against the bar.
Sibon was foiled by Edwards in the 63rd minute as he burst through only to see his low drive blocked by the Rochdale keeper.
Kevin Pressman produced a spectacular stop on 68 minutes to push away Connor's fierce effort before the lively Knight almost grabbed a second, his shot on the turn slamming into the sidenetting.
Alan Quinn was beaten by the woodwork minutes later, his shot across the face of the goal beating Edwards but skimming the foot of the far post.
Connor had another effort cut out by Pressman as battling Rochdale looked for a way back before Knight saw his close-range header touched on to the post by the Rochdale keeper.
Substitute Kevin Townson almost levelled matters minutes from time, Pressman finger-tipping his right-foot shot over the top and seconds from time Knight was foiled by Edwards at the near post