England Under-21s international Jay Rodriguez put Burnley ahead after just five minutes and then doubled the Clarets' lead with only a quarter of an hour played.
Midfielder Chris McCann then put the Lancashire side further ahead with his first league goal of the season.
Former Preston player Ross Wallace then made it 4-0 before half-time, firing in past Lee Camp.
Summer signing Ishmael Miller pulled one back for Forest shortly after the break but Charlie Austin restored Burnley's four-goal advantage to round off the win.
The result, which was Eddie Howe's side's first home win in the league this campaign, moved the Clarets above Forest in the Championship table.