Campbell opened his account for the club just five minutes into his home debut while Wallwork had to wait rather longer - two-and-a-half years to be precise.
He had been a peripheral figure at the club after his move from Manchester United before Robson recalled him to the side six games ago.
After taking the lead so early, Albion did spend much of the remainder of the game on the defensive as City made a fruitless bid to find a way back into the match.
But City lacked a cutting edge and that proved to be costly as their four-match unbeaten run in the league came to an end against an Albion side who sealed only their second Premiership win of the campaign following Wallwork's 80th minute strike.
Having survived an early scare of their own when Antoine Sibierski fired wide in the first minute, Albion made the start they had been hoping for.
A pass from Zoltan Gera picked out Martin Albrechtsen on the right wing. The Danish defender's cross was met first-time by Campbell who beat goalkeeper David James with a low right-foot shot from 16 yards.
Albion should then have added to their advantage through leading scorer Robert Earnshaw who wasted two good chances.
But City were unable to capitalise on Albion's weak finishing as Sibierski and the impressive Shaun Wright-Phillips also failed to hit the target from clear openings while Robbie Fowler fired his shot straight at goalkeeper Russell Hoult.
Albion should then really have put the game out of sight before half-time only for Wallwork to fire over the bar with Earnshaw then seeing his 43rd minute shot saved by James after a nod down by Gera.
City laid siege to the Albion goal in the opening stages of the second half only for Hoult to deny Sibierski at the near post.
Then a last-ditch clearance by Darren Purse rescued Albion with Fowler and Jon Macken both closing in on goal.
It needed a wonder save from James to keep it 1-0 in the 61st minute. A header from Campbell fell to Jonathan Greening on the edge of the area. He fired in a volley that was destined for the top corner of the net before James threw out his left hand to tip the ball over the bar.
Albion were then frustrated again in their search for a decisive second goal when Wallwork headed a Campbell cross inches wide 16 minutes from time.
But Wallwork did not have to wait much longer to get his reward for a hard working display. A move that involved Campbell, Greening and substitute Geoff Horsfield ended with Wallwork stooping low to head the ball past James from four yards.
City's dismal evening was then summed up three minutes later when Richard Dunne scored with a piledriver of a free-kick only for referee Graham Poll to disallow it as the kick had been taken too quickly.
MAN OF THE MATCH: Ronnie Wallwork (West Brom) – Produced probably his best display in an Albion shirt to justify Bryan Robson's faith in him.