Goals by Nicolas Anelka, Michael Ballack and Ashley Cole saw off the spirited resistance of the visitors who had to thank goalkeeper Brian Jensen for a string of saves that otherwise, could have resulted in double figures for the Blues.
On three minutes a sharp breakaway by the Blues saw Anelka produce a fine left footer which Jensen saved well.
Jensen then smothered the ball as Anelka ran 40 yards and tried to round the 'Beast' but the goalkeeper was equal to the task.
On six minutes, Burnley almost scored the opener when Chris McCann raced thorough from midfield but his left footer from just outside the box was inches too high.
Three minutes later Lampard was dispossessed and Tyrone Mears raced into the penalty area. He passed square to Martin Paterson who somehow slotted the ball wide of the empty goal from eight yards out.
On 12 minutes Jensen expertly blocked a Ballack shot from eight yards before saving John Terry's pile-driver.
Jensen thwarted Chelsea on 30 minutes after Terry had set up Lampard - the midfielder's volley being parried out to safety.
Seconds before the break Anelka finally broke the deadlock. Michael Essien gave an excellent throughball to Drogba on the right. The Ivory Coast hitman reached the byline and crossed the ball.
It took a touch off Steven Fletcher on its way to Anelka on the far post who lunged and prodded the ball home off the upright.
Number two came after just two minutes after the restart. Wide on the left, Anelka fed the overlapping Lampard who sailed over an inch-perfect cross to the far post where Ballack dived to head the ball past the hapless Jensen.
Then it was the turn of Ashley Cole on 52 minutes. The England international lashed the ball home past Jensen from eight yards out.
Anelka then hit the crossbar a minute later as Chelsea threatened to run riot.
The Jensen show continued to the end and the burly shot-stopper prevented Essien (twice), Drogba and Ballack from adding to the scoreline.
However, he could do nothing when Salomon Kalou's angled shot was cleared off the line by Mears with two minutes left.