The Clarets made their numerical advantage count 10 minutes later as Vokes fired in his first of the afternoon from a Matt Lowton delivery.
Goal from Sam Vokes in the 24th minute of the match gave burnley the lead.
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. Morata had a goal disallowed for offside but then Fabregas was sent off, perhaps harshly, for a tackle on Jack Cork with eight minutes remaining.
Huddersfield Town made a dream start to their debut season in the Premier League as new Crystal Palace boss Frank de Boer endured a miserable first game with a 3-0 defeat.
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.
The other key negative from the second-half was a second yellow card for Cesc Fabregas leaving Chelsea with nine men prior to David Luiz's late goal.
Morata made the flawless impact as he pulled a goal back for Chelsea in the 68th minute as he headed home Willian's cross.
While accepting that his players had been affected by the situation, Conte pointed to how they have now received red cards in each of their last three games - including the FA Cup final and Community Shield against Arsenal - but stopped short of blaming his players for ill-discipline.
Two years ago, Chelsea drew with Swansea 2-2 at home in the first match of its league title defence and quickly unraveled.
With some tough fixtures upcoming, Chelsea do not have long to put things right and must ensure they are able to regain at least some of the positivity that the club enjoyed for so much of last season.
With uncertainty over the future of Philippe Coutinho, the mantle of best player at Liverpool will fall to either Sadio Mane or Roberto Firmino, both of whom scored on Saturday. The main criticism of the Reds last season was that, while they could score with the best of them, their defense was broken down far too easily far too often, especially on set pieces.
Almost 5,000 days later, Wayne Rooney is back scoring in the blue of Everton.
Wayne Rooney marked his top-flight return to Everton after 13 years by scoring the victor against Stoke and his 199th goal in the Premier League.
No goals in a awful game at St Mary's, as Southampton toiled without fruition despite a late flurry of pressure, and Swansea failed to manage a shot on target.