After a quiet opening five minutes, Peter Whittingham sent Wales international keeper Tony Roberts sprawling to his left to push away a low ground shot.
Ten minutes later the busy Whittingham tried another shot but it lacked power and Roberts gathered.
The opening goal came in the 20th minute and once again the impressive Whittingham was involved. He slipped a pass back to the unmarked Gavin Rae who fired high into the net from 20 yards.
Five minutes later the Bluebirds doubled their lead from the spot. Jay Bothroyd was brought down by Will Antwi but his poorly taken penalty was easily saved by Roberts.
Referee Andy Penn signalled a re-take for encroachment by Dagenham and after a tussle with Michael Chopra, who also wanted to take the kick, Bothroyd drove home to extend the Bluebirds lead.
The visitors penned City back in the opening stages of the second half but despite forcing a couple of corners, they were unable to open up the Bluebirds defence. Peter Gain had their best chance but he fired wide when well placed.
When the Bluebirds did settle, they were kept out by 40-year-old Roberts who made smart saves from Miguel Comminges and Chopra.
Aaron Wildig went into midfield for Comminges in the 67th minute.
The Daggers pulled one back in the 81st minute when substitute Josh Scott met a superb cross from Antwi to turn the ball into the net for the first opposition goal at the new stadium.
The Bluebirds settled the match in the 90th minute when Whittingham exchanged passes with Stephen McPhail before beating Roberts from close range.