Rooney's absence was not felt as 18-year-old Sibley scored a first-half rocket before a Chris Martin double sealed an impressive afternoon's work for County.
All the focus before the game was on Rooney who was not in the squad although the former England captain was at the ground.
When the visitors won another in the ninth minute, the ball dropped for Brereton but he fired over from eight yards.
Derby fashioned a good opening in the 19th minute with Shinnie setting up Martin whose shot from just inside the area was pushed over.
There were strong Derby claims for a penalty in the 23rd minute when Martyn Waghorn went over but the home side took the lead four minutes later as Sibley fired an unstoppable 25-yard shot into the top right corner.
It was only a temporary reprieve because the second arrived four minutes later as Shinnie's drive was pushed out by Walton and Martin slid in the rebound.
It was almost game, set and match in the 44th minute. Waghorn went round Walton but his shot came back off the inside of a post and into the arms of the keeper.
Blackburn needed a big improvement in the second half to get back in the game but Walton had to make a smart save to turn behind a Waghorn free-kick.
Rovers won a free-kick on the edge of the area in the 58th minute but Adam Armstrong drove it into the wall and Ben Hamer made his first save of note three minutes later when he turned behind a deflected shot from Amari Bell.
Derby's defence was starting to come under pressure yet Blackburn could not find the quality or invention to get back into the match.
And their fading hopes were ended in the 85th minute when Martin converted a penalty after Jason Knight was bundled over by skipper Elliott Bennett before Buckley was sent off for a late lunge on Curtis Davies.