Dyer, a second-half substitute, demonstrated his shooting ability with a 20-yard angled shot in the 82nd minute which plunged plucky Charlton to only their second away defeat in six games.
Blues' win mirrored the success which has been generated since the appointment of Gary Rowett.
He has been inspirational and following their midweek success at Reading it was hardly a surprise that Blues were always in a positive attacking mood.
This was reflected in the fourth minute when Robert Tesche produced a speculative long-range swirling shot which Stephen Henderson finger-tipped onto the outside of the post.
Johann Berg Gudmundsson attempted a similar tactic for Charlton but it lacked the power to pose any real problem for goalkeeper Darren Randolph.
There was a spark of inspiration from Demarai Gray but the youngster was effectively stopped in his tracks by former Blues stalwart Roger Johnson.
Youngster Gray is used sparingly by Rowett, who likes to restrict him to home games when he is given to shine in front of the club's fans.
It is a policy which very nearly paid dividends in the 13th minute when his cross eluded the Charlton defenders only for Diego Fabbrini, wearing a protective face-mask, to shoot wide from close range.
The Italian was guilty of another bad miss as Blues failed to capitalise upon some good approach work.
Many of Charlton's attacks originated from Frederic Bulot, while the industry of Tony Watt kept the Blues defenders on their toes and the Scot saw his rising drive pushed over the bar by Randolph.
Both teams struggled to find the finishing touch, as highlighted by another Tesche effort deflected narrowly wide of the post just before the break.
Blues created more of the opportunities, with David Cotterill prominent.
His first effort was easily saved by Henderson while his second curling attempt hit the outside of the post after Charlton's defence had been outpaced by Gray.
It was a fair reflection of the game that Charlton were always a potential danger. Watt cleverly put Igor Vetokele clear only for Randolph to parry the striker's angled shot.
Randolph came to the rescue again to keep out another Watt effort but it was Blues who piled on the pressure in the closing stages only to be thwarted by some solid defensive work.
But it was Henderson who excelled with the best save late in the game with a diving save to keep out a goalbound header from Jonathan Grounds.
But the Irishman had no chance when Dyer was put clear by Tesche and scored with a low raking drive eight minutes from time.