Manager Thomas Tuchel made a raft of changes from the side that played a goalless draw with Wolverhampton Wanderers, with Mason Mount, Tammy, Abraham, Marcs Alonso and Timo Werner getting a look-in.
Chelsea started the game on the front foot but struggled to truly test Nick Pope in the Burnley goal. They, however, created a good chance when a cross-field ball by Jorginho found Alonso unmarked at the back post. But the Chelsea defender headed wide from a promising position.
With half-time approaching, Cesar Azpilicueta charged down the field and displayed great technique to find the back of the net after he was played in by the brilliant Callum Hudson-Odoi.
It marked the Chelsea skipper's first goal in exactly a year, and it also marked the first goal in the Thomas Tuchel era.
The second half begun in much the same way as the first, with Christian Pulisic introduced at the break for the ineffectual Tammy Abraham. Chelsea eventually got the second goal their dominance deserved when a lofted pass by Pulisic was expertly controlled by Alonso before finding the roof of the net.
The victory moves Chelsea up to seventh in the league table. On that note, let us have a look at five talking points from the game.
#5 Thomas Tuchel could deploy a wing-back system as Chelsea manager
Thomas Tuchel is widely praised as one of the most tactically savvy managers in the game.
Throughout his managerial career, the 47-year-old has shown a penchant for switching things constantly, and that has helped him achieve success.
After being unveiled as the new Chelsea manager less than a week ago, there is still room for debate over what the German tactician's preferred formation would be.
For most of his career, he has sent his teams out with a flat back four while switching things up in midfield and attack. However, on the evidence of his two games at Chelsea so far, Tuchel seems inclined to play with a three-at-the-back system.
That means the use of wing-backs, rather than full-backs and an emphasis on overloading the midfield. If that indeed happens to be the case, it would not augur well for traditional wide man like Hakim Ziyech and Christian Pulisic.
It remains to be seen what Tuchel's likely formation would be, as 180 minutes is too small a sample size to make an informed decision. However, having started out with a wing-back system, this might well be the formation Chelsea could deploy moving ahead.
#4 Callum Hudson-Odoi enjoying life in new role
As already indicated, the full-back system requires wing-backs to man the wide positions, and Callum Hudson-Odoi seems to be Thomas Tuchel's go-to man in this position.
The England international has started both games in this position. After being the star of the show against Wolves, he followed up with yet another captivating display.
The 20-year-old was unplayable on the Chelsea right flank, giving Eric Pieters a torrid time in the 73 minutes he spent on the field.
It was his brilliant play that led to the opening goal for Chelsea; Hudson-Odoi also hit the post and created several chances for his teammates.
Overall, Callum Hudson-Odoi had three key passes in the game and was arguably the Man-of-the-Match for Chelsea. He got himself into great positions throughout the game and seems to be living up to the demands expected of him from his new manager.
After struggling to impose himself in the Chelsea first team over the last two years, Hudson-Odoi might have found a new role that he could be more suited to.
In many ways, it draws similarities with another winger who enjoyed a new lease of life after being converted to a wing-back in the past. Former Nigeria international Victor Moses also struggled to get much playing time before playing a key role in the title win under Conte as a wing-back.
It is unknown if Thomas Tuchel will stick with this system moving ahead, as Reece James also deserves an opportunity to show what he is capable of. However, on evidence of the two games Chelsea have played under their new manager, Callum Hudson-Odoi could be a key man in this system.