Scotland striker Miller opened the scoring in the 19th minute with a low left-footed finish and Gerrard sealed the win by nodding home five minutes after the break after Blackburn keeper Mark Bunn had failed to deal with a corner.
At the other end David Goodwillie had his headed effort well saved by Cardiff keeper Tom Heaton and Scott Dann also nodded wide, but in truth Rovers were well beaten and the visiting support made clear their dissatisfaction with repeated chants of “Kean out”.
The match started scrappily as the visitors carved out the opening chance when Morten Gamst Pedersen’s clever lay-off saw Goodwillie shoot across the face of goal.
Blackburn’s early dominance continued when Heaton was forced into a sharp save as Grant Hanley hit the target with a header from a Pedersen corner, but the Norwegian gifted the hosts the lead in the 19th minute.
Aron Gunnarsson seized on a poor pass by Pedersen to play Miller in to beat Bunn with a low left-footed finish.
Cardiff had appeals for a penalty waved away early in the second-half despite Mauro Formica making a clumsy challenge on Peter Whittingham on the edge of the box.
But it only proved a brief reprieve for the visitors as Cardiff doubled their lead through Gerrard.
Bunn came for a Whittingham corner and got nowhere near it as Ben Turner headed back across goal for his defensive partner to finish.
Midfielder Filip Kiss had a great chance to further extend the lead but headed wide, with the travelling support voicing their displeasure.
Miller fired high and wide after being teed up by Gunnarsson’s intelligent pass before Dann came within inches of giving Rovers a lifeline as he glanced a header just wide.
Kean threw on Aiyegbeni Yakubu and Jason Roberts for the closing stages and the Nigerian’s first act was to attempt to square the ball in the area despite having the space to get an effort in on goal.
Fellow substitute Ruben Rochina then curled wide from distance to cap a miserable night for the visitors.
CARDIFF: Heaton, McNaughton, Taylor, Gerrard, Turner, Kiss (McPhail 78), Whittingham, Cowie, Conway (Ralls 83), Gunnarsson, Miller.
BLACKBURN: Bunn, Givet, Dann, Hanley, Dunn, Formica, Pedersen, Petrovic (Rochina 70), Lowe, Blackman (Roberts 80), Goodwillie (Yakubu 80).
Ref: Martin Atkinson.