Hull took the lead on 14 minutes as Campbell made space for himself inside the Burnley box and hit a right-footed effort from 10 yards which saw the ball sneak under the body of keeper Brian Jensen.
Phil Brown's men were nearly two up soon after as Okocha played a superb through ball to Campbell, who raced onto it inside the Burnley box.
However, the Manchester United loanee couldn't finish the chance off as his left-footed shot from six yards whistled past Jensen's left-hand post.
The Tigers were 2-0 up on 28 minutes as Garcia found himself in space 30 yards from goal and the Hull man fired in a right-footed shot which saw the ball rocket into the top right corner.
In the space of two minutes midway through the second half both sides were down to ten men as referee Mike Riley gave Folan a straight red card for an off-the-ball incident in the Burnley box.
Seconds later visiting captain Caldwell received his second yellow card of the game for a professional foul just inside the Hull half.
Burnley nearly grabbed one back moments later as Andy Cole rose to a curling cross from the right, but his looping header from close range came back off the crossbar.
Then minutes later both teams were down to nine men as both Okocha and Gudjonsson were sent off for another off-the-ball incident. Okocha was given a straight red card and Gudjonsson picked up his second yellow in ten minutes.