Both sides started brightly, with Ian Henderson having an early shot blocked for the Lancashire club and Jose Baxter heading over for the hosts inside the first 10 minutes.
Henderson again threatened with another effort for the visitors, while Stephen Dawson also squandered a chance to give Keith Hill's men the lead.
Dale continued to press for an opener, with Matt Done forcing a save out of Mark Howard as the Blades struggled to repel the away side in attack.
However, the hosts began to threaten the Rochdale defence, with Jamie Murphy and Baxter again having chances to give Nigel Clough's men the advantage, before Neill Collins headed over on the stroke of half time.
Within moments of the restart, United nearly edged in front when Campbell-Ryce, preferred in attack to Ryan Flynn and Marc McNulty, flashed an effort inches wide of Conrad Logan's post.
Nigel Clough's charges continued to trouble Rochdale after the break and Chris Basham nearly breached the Rochdale rear-guard with a header from the heart of the area.
It was left to Campbell-Ryce to finally break the deadlock when his shot from the left side found the top corner of Logan's net, to the relief of many inside Bramall Lane.
The result leaves Sheffield United only a point off the League One playoff positions, while Rochdale are just two points ahead of the relegation zone.