The summer signings both shined for the Blues against their newly promoted hosts, with the 32 million pound striker on the scoresheet and his compatriot providing two assists.
After falling behind to a stunning early strike from Burnley midfielder Scott Arfield, Jose Mourinho's side slipped through the gears to dish out a top-flight lesson to its newly promoted hosts - with new signings Diego Costa and Cesc Fabregas shining.
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Striker Costa opened his Premier League account with an equalizer just three minutes after Arfield's opener, and former Arsenal captain Fabregas assisted goals for Andre Schurrle and Branislav Ivanovic before the break.
Fabregas produced a moment of real quality with a stunning pass into Schurrle for Chelsea's second goal after 21 minutes, and the impressive Ivanovic then tucked away the Spaniard's corner 13 minutes later.
Chelsea took its foot off the pedal somewhat in the second half, but its ruthless response to falling behind should serve warning to the other Premier League title contenders.
Thibaut Courtois made his debut in the Chelsea goal after being selected ahead of long-term number one Petr Cech, but the Belgium international could do little to prevent Arfield from rewarding Burnley for an impressive start in the 14th minute.
The 25-year-old met Matthew Taylor's cross from the left byline with a fierce half-volley that flew past a stranded Courtois to send the home crowd into raptures.
However, Burnley's shock lead did not last long, as Costa produced the kind of finish that led Chelsea to splash out a reported 32 million pounds to recruit him from Atletico Madrid with a powerful low shot into an unguarded net after Ivanovic's right-wing cross had crashed against the far post.
Mourinho's men then completed a seven-minute turnaround in wonderful fashion with a mesmerising team move that saw Schurrle coolly slot home from Fabregas' sumptuous first-time pass following neat link-up play from Eden Hazard and Ivanovic.
Chelsea was aggrieved not to have been awarded a penalty nine minutes later when Costa appeared to be taken down by Burnley keeper Tom Heaton after latching on to Ben Mee's poor back pass, with referee Michael Oliver instead opting to book the forward for diving.
But, after playing an integral role in the first two Chelsea goals, right back Ivanovic put the visitors in command, capitalizing on sloppy marking to convert Fabregas' set piece.
Burnley came into the second half with renewed vigor and immediately came close to halving the deficit when Courtois tipped Arfield's long-range drive over the crossbar.
Neither side created too much in the way of goalscoring opportunities as the visitors saw things out with little difficulty, with the away end's largest cheer of the second period coming when club legend Didier Drogba made his second Chelsea debut as a late substitute.
Despite the result, Burnley boss Sean Dyche will have been heartened by his side's industry and spirit ahead of a tricky trip to Swansea City on Saturday.
Yet the plaudits will rightly go to Chelsea, which looks ready to make good on Mourinho's pledge to be there or thereabouts when the Premier League trophy is dished out in May.