Goal from Sam Vokes in the 24th minute of the match gave burnley the lead.
Vokes then grabbed his brace and the third for Sean Dyche's men when he headed in the ball from a Defour cross two minutes before the half time break.
Fellow midfielders Tiemoui Bakayoko and Eden Hazard have already been ruled out of the opening weeks of the season.
The second half will shut will show whether the 10 man Chelsea could turn the match around.
Meanwhile, Chelsea's biggest competitors this coming season, Manchester City and United, have spent £405m in the transfer market thus far and both Pep Guardiola and Mourinho, arguably, now have the squads they have been building steadily towards.
The Clarets survived in the Premier League due to a strong home record last season but were atrocious away from Turf Moore, winning just one game throughout the campaign. While he is probably hoping that will jolt Roman Abramovich into action, it now appears to be having more of an effect on his players than his owner.
Frank Lampard sends message to Man United fans about midfielder
Matic was frustrated with the result but has called on United to turn their full focus to Sunday's league opener against West Ham. Chelsea manager Antonio Conte has described the departure of Nemanja Matic as a "great loss".
But it all fell apart for the Blues on 14 minutes when skipper Gary Cahill was given a straight red for a reckless challenge on Steven Dafour.
Chelsea fought back to score two goals, but were reduced to nine men when Cesc Fabregas was dismissed and were unable to net an equaliser.
Chelsea now face suspensions ahead of crucial games against Tottenham, Leicester and Everton.
But really this was a disastrous start for the champions, an opening day defeat that some will suggest came heavily trailed.
Cahill was made club captain following the departure of long-serving skipper John Terry at the end of last season. More results away from Turf Moor will be needed this term but this was a magnificent start to life without Michael Keane and Andre Gray. They still had the quality to peg Burnley back, particularly as the visitors exhausted as the second half wore on, but lacked subtlety in their approach.
Despite the dire performance, the majority of the 41, 616 fans still cheered head coach Antonio Conte's name from the stands. He scored off a Willian assist and then helped David Luiz to a goal with five minutes to play. Chelsea will need it.