The Cherries took the lead within the first two minutes of the game, as Simon Francis was able to unleash a volley from the edge of the Leeds area following a corner kick.
The ball subsequently deflected off Yann Kermorgant and into the net for the first goal of the match.
Midway through the first half, the home side doubled their lead as a low cross from Francis, following a swift counter-attack, was directed home by Lewis Grabban.
The third goal came just before the half-hour mark, as Francis was able to maraud into the Leeds area and, with a deft backheel, set up Grabban who lashed the ball past Jack Butland.
The Cherries then compounded the misery for the Yorkshire side when, six minutes after the restart, Kermorgant met Matt Ritchie's cross with a powerful header to make it 4-0.
The away side did however net a consolation midway through the second half when Ross McCormack struck a neat finish from the edge of the box.