The home side thought they'd scored on the half-hour mark as Ian Ashbee headed in a neat cross from David Livermore, but the linesman ruled Livermore to be offside.
Wolves came close to scoring in the closing stages of the half as frontman Freddy Eastwood struck an arrowed shot from 20 yards which was deflected just wide.
Hull took the lead just after the break as Bryan Hughes played a smart through ball to Campbell on the left of the box. The Manchester United loanee then played a ball across the box towards Garcia, who hit a right-footed effort from ten yards which found its way through the legs of Wayne Hennessey and into the back of the net.
Phil Brown's men doubled their lead on 61 minutes as Hughes did well down the left to lay a clever ball off to Andy Dawson, who swung in a curling cross into the box towards Garcia. His header was palmed out by keeper Hennessey, but only to the feet of Campbell, who swept up the rebound from close range to make it 2-0.
As Hull started to take the foot off the gas, Campbell was still hungry for more as he ran from the half way line, skipped several challenges and fired in a shot, but his right footed effort from 20 yards was saved by Hennessey.