Sam Vokes scored twice, continuing the superb form he finished last season in, while Stephen Ward netted a stunning half volley as Burnley went in 3-0 up at half-time, capitalising on the early dismissal of former Claret Gary Cahill.
Conte feared Chelsea were less than ready for this title defence, admitting on Friday he agreed with those who did not list his team among the favourites to win the Premier League.
Chelsea are expected to make new signings before the end of the transfer window with British media reporting that Conte is dissatisfied with the depth of his squad.
Tom Ince missed an early chance to give the Terriers the lead when he sent a bouncing effort from Tommy Smith's cross straight at keeper Wayne Hennessey. With Eden Hazard, Tiemoue Bakayoko and Pedro Rodriguez injured and Victor Moses suspended, Chelsea had a threadbare match-day 18.
Spanish worldwide Alvaro Morata came from the bench to score the first goal for the Blues in the 69th minutes before David Luiz netted at the death as the match ended 3-2 in favor of Burnley.
But Rooney ended a scrappy first half when he headed in to mark his Goodison homecoming in the best possible style. He scored off a Willian assist and then helped David Luiz to a goal with five minutes to play. Disjointed and embarrassed in the first half, Chelsea threatened to mount the most unlikely of comebacks in a stirring second-half display, but just failed to overcome their numerical disadvantage.
That didn't stop the Blues from making it 3-2, as Morata flicked onto Luiz for a cool finish.(NBC Sports).
"That's a huge result - a lot was made of our away from last season", he said. Vokes had a goal disallowed shortly after - but it was an omen for Chelsea. Burnley may not be a sustainable Premier League club in the long term, but Dyche is a highly competent top-flight coach, more motivated than most by the desire to overcome the odds and confound his critics.