Fabregas had been shown a yellow card for dissent before a tackle on Jack Cork ended his afternoon.
The 27-year-old is interested in leaving Leicester for the Premier League champions, which Conte hopes will convince the Foxes to part with the midfielder when the Blues return with their improved offer. Antonio Rüdiger played on the left of the central three in defence. His roaming run into the opposition half, perhaps an attempt to grab the game by the scruff of the neck, was fine, but his lunging tackle into Defour was clumsy and risky and left the referee with no option but to send him off. Cahill overstretched as he missed the ball. Precedents suggest it was fair, although it was by no means a vicious foul.
In-form Vokes now has seven goals in his last six Premier League appearances after netting only five in the previous 58.
Burnley went for the fourth goal but the post kept out a 90th minute freekick as the defending champions sought an equaliser.
Matt Lowton's right-wing cross found Vokes and he sent a bouncing volley into the far corner, with Thibaut Courtois unable to get across in time.
Spurred on by Cahill's dismissal, Burnley surged into a 3-0 half-time lead at Stamford Bridge courtesy of two goals from Sam Vokes either side of a spectacular Stephen Ward strike, and Chelsea could not salvage a draw despite a debut goal for Alvaro Morata and David Luiz's volley in the second half.
Townsend backing promoted Brighton to survive then thrive in Premier League
Diame had to choose between Premier League football with Hull - and another season in the Championship with Newcastle United . Pascal Gross has urged Albion to keep their wits about them for 90 minutes and beyond against Manchester City .
Next up for Chelsea is a tricky trip to Wembley to face Tottenham Hotspur next weekend.
Things fall apart. The centre can not hold. Within three minutes it was 3-0, with another simple goal: another cross from the right by Defour, another bad piece of marking by David Luiz, and another simple headed finish by Vokes in hectares of space. Alonso had a fierce free kick well saved by Tom Heaton just after the hour mark.
Chelsea's second goal came two minutes before full time.
That does not sound like a man bursting with confidence, more so when you realise that his "Special One" jibe refers to the Portuguese mentor's disastrous 2015/16 season with the Blues.
Conte returned to his mantra from last season that the team needed to work hard to produce results and he pointed out that Chelsea had finished their last three games without all 11 of their players on the pitch.