Burnley enjoyed two half-chances early on through Chris McCann and Martin Paterson, but the first real chance of the match fell to Bolton's Lee Chung-Yong. However, the South Korean scuffed his chance from 12 yards out and the ball trickled past the post.
The hosts took the lead with five minutes left of the first half as Junior Stanislas and Dean Marney both had shots blocked before Charlie Austin set up Peterson for a close-range header that he couldn't miss.
The lead was doubled ten minutes into the second half when Stanislas whipped a cross in from the left that was met by Austin's header.
Burnley's next match comes away to Middlesbrough on Tuesday evening, while Bolton will take on Derby that night too.