The Blues defeated Werder Bremen 2-0 at Stamford Bridge two weeks ago and, after claiming three points in Bulgaria, the odds are now firmly on the Premiership champions qualifying alongside Barcelona with ease from Group A.
Drogba's opening strike six minutes before the interval capped an unspectacular first-half display as the Ivory Coast striker followed up with a simple tap-in after Georgi Petkov had acrobatically tipped away a close-range shot from John Obi Mikel .
The goal was Drogba's fifth in seven games, but the lively frontman should have given Chelsea a 16th-minute lead when he crashed a half-volley from 10 yards against the crossbar.
Michael Ballack was next to test the home goal as he dispatched a powerful 30-yard drive only to see his effort palmed on to the post by the athletic Petkov.
Levski enjoyed plenty of possession but rarely threatened Petr Cech in the Chelsea goal and their failure to impress in the final third was punished seven minutes into the second half.
Wayne Bridge lofted a long ball down the centre and, after giving his marker the slip and prodding a low shot goalwards, Drogba watched nervously as Petkov got his body to the ball but could not stop it trickling over the line.
Fifteen minutes later Drogba completed the scoring for the visitors with a neat flick past the stranded Petkov after the home defence had allowed Frank Lampard time and space to shoot from the edge of the box.
Cech proved his class late on with a series of saves from Hristo Yoyov, but he was beaten in the final minute when substitute Mariyan Ognyanov was allowed to run through the middle and latch on to a simple pass before drilling the ball home from 15 yards for a consolation effort.
But, despite the late disappointment, it was a comfortable night for Chelsea and one they are unlikely to experience in the next few weeks with back-to-back clashes against Champions League adversaries Barcelona to come.