Although Barnsley dominated possession for long spells they failed to really test Tigers keeper Boaz Myhill, before Dean Marney tucked away the third in the dying seconds.
Campbell, who was making his home debut for Hull, got the hosts off to a flying start when he latched on to a precise through-ball from Dean Windass to slot home a right-footed shot.
Moments later Richard Garcia forced Heinz Muller into a smart reflex save with a close-range toe-poke, but Hull did not have long to wait for their second. Campbell collected a pass from Marney on the edge of the area and wriggled past two defenders, before scoring with an excellent angled shot with his right foot into the bottom left corner.
Barnsley looked anxious in defence and short of ideas in attack with a deflected free-kick from Anderson Silva their only real attacking moment of note in the first period.
Things improved for Barnsley in the opening stages of the second half, but although they penned Hull back, they were unable to carve open a stubborn home defence.
Silva surged forward and hit a low right-footed drive wide of the mark, before a wayward cross from substitute Martin Devaney nearly caught out Myhill.
However, Hull, who hit the post early in the second half through David Livermore, always looked dangerous on the break.
In the first minute of stoppage time, substitute Stephen McPhee raced clear and played in Marney, who slid the ball underneath Muller to round off the win for the home side.