Joe Ledley struck twice in the first half and Paul Parry added a third early in the second period. Patrick Agyemang notched a consolation for the visitors who ended up well beaten.
Bluebirds skipper Stephen McPhail failed a late fitness test on his injured hip and so Aaron Ramsey slotted into midfield. The only other change from the side that won at Hereford was the return of Jimmy Floyd Hasselbaink up front for Steve Thompson.
City made full use of the wings to press the visitors back on defence with Ledley and Parry causing problems with their direct running.
The goal they deserved came in the 12th minute when Damien Delaney hit a poor back pass. Parry raced on to the loose ball and crossed to the waiting Ledley, who slotted home from close range.
Visitors keeper Lee Camp produced tremendous saves midway through the half from both Peter Whittingham and Hasselbaink as City went looking to increase their lead.
The second goal arrived in the 39th minute with Ledley's second of the evening. Ramsey sent a pass out wide to Hasselbaink and he slipped the ball into Ledley who made no mistake.
It only took City 12 minutes into the second half to go further ahead.
Glenn Loovens flighted a ball down the middle, it was worked through to Parry and he easily beat Camp from 15 yards.
A rare Rangers attack in the 75th minute led to a goalmouth scramble and a consolation goal for the visitors.
Michael Oakes was laid out in the attack as Agyemang forced the ball home from in front of the posts.
Oakes had to leave the field and Peter Enckelman replaced him to make his Bluebirds debut.
City suffered some anxious moments as the game drew to a close and Roger Johnson hooked one goalbound strike off the line, but the Bluebirds ran out worthy winners.