With Rovers' defence in disarray, Jermaine Beckford hit a post and missed three other opportunities before Bradley Johnson opened the scoring in the 14th minute.
Luciano Becchio leapt to meet Jonny Howson's right-wing cross and although Daniels parried the Argentine's header, Johnson despatched the ball past him first time from a tight angle.
With Howson running the game from central midfield, chances continued to be created for Beckford and he eventually capitalised with his fourth of the season. With 35 minutes gone, Ian Goodison headed towards his own goal, allowing Beckford to nip in and send his shot in off the foot of the far post.
The blameless Luke Daniels made a superb save to prevent Johnson grabbing his second shortly before half-time.
Beckford fired against the crossbar in the 54th minute, Becchio's header struck a post and when Johnson hit the woodwork, Becchio headed in the rebound for Leeds' third.