However, the away side pulled a goal back midway through the first half, courtesy of a volley from Danny Ings.
Harry Redknapp's team took the lead for the second time in the half with just over 10 minutes to go, as veteran defender Richard Dunne fired a left-footed shot into the top corner.
Burnley went from a goal down to a goal up in the space of eight second-half minutes, as Sam Vokes bagged two goals in quick succession. The first saw the Welsh striker beat Dunne to head Kightly's cross into the near corner, while the second was helped by a Benoit Assou-Ekotto error.
However, the game would provide more action. With 11 minutes to go, Modibo Maiga was gifted with an easy chance, courtesy of some good work by Hoilett and some haphazard Burnley defending. The Mali international duly scrambled the ball into the net to make it 3-3.
The ball, however, bounced just wide of the goal.