The Bees, who had three of their summer signings starting, flew out the traps and should have gone ahead after just 40 seconds when Isaiah Rankin cut inside the last defender before firing a tame effort at Scunthorpe's Paul Musselwhite.
Scunthorpe replied minutes later when a fine move down the right-hand side resulted in Richard Hinds' cracking shot being superbly turned away by Stuart Nelson in the home goal.
Chances after that were at a premium though Bees skipper Michael Turner and Scunthorpe's Cliff Byrne were forced to make dramatic defensive clearances.
The half ended with one more chance for the home side as from Paul Brooker's corner, Eddie Hutchinson's flick-on struck the post with Jay Tabb firing the rebound over.
The second half began with a PR announcement for a fourth official and having been found, it was the visitors who started brightly.
In the first of three chances in the opening minutes some fine play from Matt Sparrow saw him tee-up Ian Baraclough whose precise shot struck the post.
Cleveland Taylor then horribly fired over from eight yards after the ball fell invitingly for him from a corner before Turner under hit a back-pass to Nelson but Steve Torpey couldn't prod it past the keeper.
Scunthorpe continued to create the chances with Taylor's deflected shot bringing out a fine save from Nelson before they had a great shout for the opener when Andy Crosby's header from Baraclough's corner seemed to have crossed the line.
However, despite the chances, the Bees took the lead in the 71st minute when great persistence and closing down from substitute Campbell saw him play in Tabb who scored with an emphatic finish.
Ten minutes from the end, Hutchinson's goal-bound shot struck a Scunthorpe hand in the box and Campbell stepped up and fired home the spot-kick.