The Blues' win was influenced by the magnificent Christian Pulisic who bagged not only his first goal for Chelsea, not just a brace but the 'perfect hat-trick' in a perfect trip to Turf Moor.
The three points see Chelsea consolidate their position in fourth as they sit behind Leicester City on goal difference, as the pair sit on 20 points.
Frank Lampard made one change from his side's 1-0 win over Ajax in midweek - also influenced by Christian Pulisic - and the 21-year-old was rewarded with a start, ahead of Callum Hudson-Odoi.
Pulisic took his chance and sent Chelsea on their way to all three points in Lancashire. The 21-year-old scored his first midway through the first-half with an excellent run, which was capped off with a fine finish on the USA star's left-foot past Nick Pope.
But he added another just before half-time, this time on his right. A deflection helped it through for the 21-year-old to bag his first two goals for the club since joining from Borussia Dortmund.
Chelsea showed their ruthlessness and put their chances away, and it was the same old story in the second-half.
Pulisic was back in the action, and completed his hat-trick, the 'perfect hat-trick' as his third was via the little man's head!
Willian added a fourth for Chelsea with another excellent finish for the Blues and that all but secured all three points for Frank Lampard, as the Blues continue their fine form, and bag their seventh consecutive win in all competitions.
Jay Rodriguez pulled one goal back for Burnley with a fine effort, leaving Kepa Arrizabalaga with no chance. McNeil then got the second for the home side in the final stages as the hosts produced a late comeback.
But it was too little too late from Sean Dyche's side, and Chelsea walked away with the points, despite the disappointing end to the game having conceded twice.
Who will get past this Chelsea side, and take points off of them?