The Blues were forced to come from behind to get the victory as Scott Arfield smashed home a volley to give the Clarets a shock lead after less than quarter of an hour.
Here, Sports Mole takes an in-depth look at an intriguing 90 minutes in Lancashire.
On target: 2
On target: 3
Was the result fair?
Absolutely. Burnley played pretty well this evening, but they can have no complaints at having ended up on the losing side. The hosts began the match really brightly and deserved their lead, but from then on Chelsea were in control.
The Blues stepped up a gear having fallen behind, and it didn't take them long to overturn the deficit. They played some magnificent football in the first half and were simply the better team tonight. Both teams played well, but Chelsea's quality shone through, and that was the difference.
It could have been worse for Burnley had the visitors kicked on in the second half, but Jose Mourinho seemed happy to protect the two-goal advantage. That made the second 45 minutes something of a disappointment, but Chelsea did what they needed to do before the break to take home all three points.
Despite the result, Burnley can go home very pleased with how they performed this evening. They were particularly impressive in the opening 10 minutes or so, and deserved their lead when Arfield scored in the 14th minute.
They were simply unable to cope with Chelsea's ability to move up a few gears, but that won't worry Sean Dyche too much. The Clarets were arguably handed the toughest opening weekend assignment of all and they will know that easier tests are to come over the next nine months.
If they can play like they did today all season then they could well be a surprise package once again. They have been heavily tipped for an immediate return to the Championship this term, but Dyche can take plenty of positives out of their performance tonight.
Very impressive. They have set down a marker for their fellow title contenders now, putting in the best opening performance of anyone in the league so far. The second half was a rather dull affair as Chelsea merely looked to protect their lead through controlling the tempo of the match, but it was all about the opening 45 minutes.
The first half contained enough moments to back up why Chelsea are considered favourites for the title this season. They played some exquisite football, passing the ball around well and looking like a perfectly balanced team. The second goal was a thing of beauty, and that summed up how the Blues were playing at that point.
A minor concern will be the slow start and falling behind, but that is a very small issue considering the positives to have come out of this match. Bigger and harder tests will certainly come, and it is important not to get carried away with an opening win over a newly-promoted side, but Chelsea do look ominous.
Sports Mole's man of the match
Cesc Fabregas: What a return to English football. All of Chelsea's new signings looked impressive, but Cesc Fabregas simply ran the show from midfield. He was magnificent in almost everything he did, influencing the game in attack when Chelsea wanted goals and keeping the ball in midfield when they didn't.
There were a number of majestic moments throughout the match from the former Arsenal and Barcelona man, but none more so than his pass for the second goal. Having set up to shoot first-time from the edge of the box, he instead clipped an inch-perfect pass through for Schurrle to finish. It was sublime.
This dubious honour goes to Ben Mee for a suicidal back-pass that his side were very lucky to get away with. With the score still 2-1, he undersold his keeper with a pass, allowing Costa to nip in and win the ball.
The striker took it past Tom Heaton before going down inside the area and claiming a penalty. The referee instead controversially booked Costa for a dive, leaving Mee as the most relieved man inside Turf Moor.
That penalty incident was the biggest moment of an otherwise quiet night for Michael Oliver. Costa was unfortunate to have been booked as there was certainly contact, but the penalty decision itself could have gone either way. It looks more like a penalty the more you see it, but on first viewing it did appear that the debutant striker had gone down theatrically.
Burnley: Burnley will be looking for their first points back in the Premier League when they face Swansea City at the Liberty Stadium on Saturday.
Chelsea: Chelsea, meanwhile, have another newly-promoted side to face next as they host Leicester City at Stamford Bridge, also on Saturday.