The victory, only Albion's second in 16 league games under the control of manager Bryan Robson, lifted them off the foot of the table for the first time since November as they jumped over Norwich City.
It also moved them within five points of fourth from bottom Crystal Palace.
Albion controlled the game for long periods against a disappointing Blues side who weakly surrendered the proud local derby record of their manager, Steve Bruce.
It was the first time he had been beaten in 11 derby games in charge of Birmingham in the Premiership and came hard on the heels of another poor performance in their last match at Palace, which they also lost 2-0.
The only real surprise was that Albion had to wait until the 53rd minute for Clement to break the deadlock with his third goal of the campaign and his first since the second game of the season against Aston Villa.
One goal looked to be enough to see off Birmingham, but veteran marksman Campbell put the result beyond doubt with the second 11 minutes later.
Albion dominated proceedings in the first half but were unable to turn that pressure into what would have been a deserved breakthrough.
Birmingham spent the majority of the opening period penned in their own half and the fact that Albion goalkeeper Russell Hoult did not have a save to make told its own story.
The closest that Birmingham came to troubling Hoult in the first 45 minutes was when full-back Olivier Tebily, who was later to limp off with an ankle injury, sliced a cross shot well wide.
On-loan Manchester United midfielder Kieran Richardson ran the game for Albion only to be frustrated by the woodwork for the second successive game at home.
Central defender Clement twice went close with early long-range drives before Richardson started to influence matters.
Albion were unfortunate not to break the deadlock in the 13th minute when Geoff Horsfield's cross shot was beaten into the path of Campbell by goalkeeper Maik Taylor.
Campbell's snap shot was goalbound only to be cleared off the line by left-back Jamie Clapham.
Richardson then did beat Taylor three minutes later only to see his 25-yard drive crash off the post.
Zoltan Gera met a 19th minute cross from Richardson with a powerful header only to see Northern Ireland international Taylor tip the ball over the bar.
Richardson also tried his luck from long range in the 30th minute only to see his effort drift wide.
But Albion's persistence was finally reward eight minutes into the second half thanks to the persistence of Gera.
His efforts in chasing what looked like a lost cause earned Albion a corner which Richardson floated into the box.
Clement rose above the Birmingham defence at the far post to crash home a header from ten yards.
The shock of falling behind finally work Birmingham from their slumbers and they were only denied an equaliser two minutes later by the post.
Stan Lazaridis, a first-half replacement for the injured Tebily, twisted and turned on the left-hand edge of the Albion area before floating a cross on to the head of Emile Heskey.
The England international striker steered his header beyond Hoult only to see the ball roll to safety off the foot of the post.
It proved to be a crucial miss as Albion put the result beyond doubt through Campbell in the 64th minute.
Albion's former Birmingham striker Horsfield muscled the ball off City skipper Kenny Cunningham and fed the ball to Jonathan Greening on the left wing.
Greening floated over a cross that left Taylor rooted to his line and Campbell nonchalantly sidefooted the ball home at the far post for his third goal since arriving on a free transfer from Everton in January.
Campbell then missed a golden chance to grab his second five minutes before full-time when he headed a Horsfield cross wide from just seven yards.