Goals from Youssouf Mulumbu, James Morrison and Paul Scharner clinched a 3-1 victory and enabled the Baggies to leapfrog their local rivals in the battle for Barclays Premier League survival.
All the home side could manage was a consolation effort from Jean Beausejour, as they paid the price for some uncharacteristic but sloppy defensive play.
The introduction of Albion striker Peter Odemwingie at half-time made a massive difference up front for the visitors and he was a constant threat.
But Hodgson has also made West Brom more difficult to beat after they had shipped goals regularly before his arrival.
Scharner produced a superb performance in the centre of the park while Steven Reid impressed at right-back and got forward to good effect.
Birmingham boss Alex McLeish will be hoping his side recover quickly from this setback otherwise their top flight status could be seriously threatened.
McLeish made five changes - three enforced through injury - after the Wembley triumph.
There was a carnival atmosphere amongst the Blues fans after the defeat of Arsenal.
But Albion were the first to settle and Chris Brunt had the first attempt on target, although his header from Jerome Thomas' centre did not extend Ben Foster.
A mistake by Roger Johnson let in Thomas for another run at goal but his shot was blocked.
Blues started to get a foothold in the game and an error by Scharner almost proved costly for Albion as his misdirected pass was seized on by Cameron Jerome. The striker's low shot beat the dive of Scott Carson but flew just past the far post.
Thomas and Brunt had an angry exchange after the former waited to long before playing in a team-mate.
Jerome missed a golden chance to put Blues ahead after 36 minutes. Jean Beausejour got the better of Abdoulaye Meite before floating over an inviting cross which picked out the returning Jerome - but from 10 yards out he glanced his header past the post.
Hodgson brought on Odemwingie for the second half and he made an instant impact in setting up the opening goal for Mulumbu in the 47th minute. The substitute's pass was perfectly timed for Mulumbu to flick the ball wide of Foster and into the net.
Blues responded immediately and equalised within a minute through Beausejour, who nipped in between two defenders to steer home a cross from Lee Bowyer.
Bowyer was booked for a challenge on Mulumbu and Liam Ridgewell and Scharner joined him in the referee's notebook after they wrestled each other to the ground on the edge of the Birmingham box.
A superb strike from Morrison restored Albion's lead in the 58th minute. Reid made good ground before finding Morrison, who cut inside Curtis Davies and volleyed left-footed past Foster.
Odemwingie missed a great chance to double the visitors' advantage after 67 minutes. Brunt's shot hit the post and fell to Odemwingie unmarked 10 yards out - but he fired over the bar.
With 18 minutes remaining Scharner made it 3-1. Blues failed to pick up Brunt from a short Morrison corner and his centre was headed over the line by Scharner from an acute angle at the far post.
Blues were at sixes and sevens and Foster was able to get back just in time after Scharner had spotted him off his line.
Odemwingie could have made it 4-1 after peeling away from Johnson to meet a cross from Brunt - but he headed back across goal.
Keith Fahey was booked in the closing seconds for a challenge on Reid - and by then the game was beyond the home side.