The Blues made light work of Burnley in Eden Hazard's absence — the Belgian was missing with a back problem — as a devastating attacking display saw off the Clarets and moved Maurizio Sarri's side up to second in the table, two points behind leader Liverpool.
Barkley's deft pass in the 22nd minute set Morata up for Chelsea’s opener and the England international scored in his third consecutive Premier League game 12 minutes into the second half to put the game beyond Sean Dyche's side.
Willian added a third after 62 minutes with a wonderful finish from distance and Ruben Loftus-Cheek scored his fourth in two games as Chelsea cruised to a victory that leaves Burnley languishing in 15th.
Joe Hart had to be alert to deny Chelsea a 12th-minute opener, the Burnley goalkeeper pawing away Morata's instinctive header from Barkley's scuffed shot.
Robbie Brady, who was making his first appearance in 10 months after a knee injury, then flashed wide for the hosts before Willian went agonisingly close to breaking the deadlock, his precise effort coming off Hart's left-hand post.
There was no such luck for the Clarets in the 22nd minute when Morata slotted into the bottom-left corner after latching onto Barkley's incisive through-ball.
Morata then squandered two golden chances to cement Chelsea's superiority before the interval, first dragging wide after cutting inside Ben Mee and then firing straight at Hart after being picked out by Jorginho.
The rejuvenated Barkley doubled Chelsea's advantage in the 57th minute, bursting forward from midfield and drilling into Hart's bottom-left corner from 25 yards.
That was followed just five minutes later by a third from Willian, who cut in from the left and whipped a fine strike past Hart for his second league goal of the campaign.
Fresh from his hat-trick against BATE in the UEFA Europa League, Loftus-Cheek slammed home a fourth from close range in stoppage-time as Chelsea sent out an ominous statement about its title intentions.
Chelsea hosts club legend Frank Lampard's Derby County in the Carabao Cup in midweek, while Burnley's next match is a visit to West Ham United in the Premier League next weekend.