Eden Hazard scored twice while Loic Remy, Didier Drogba, John Terry and a Mitja Viler own goal completed an emphatic win for Jose Mourinho’s side who remain unbeaten this season.
Remy gave Chelsea the early lead, scoring his first goal in the competition for almost three years, before immediately being forced off due to injury.
His replacement Drogba didn’t have to wait too long to get his name on the scoresheet following a dubious penalty decision. The Ivorian stepped up to score his 43rd Champions League goal.
It was Drogba’s first Chelsea goal since his decisive strike in the 2012 Champions League final and his 158th Blues goal – he netted 157 goals in 341 appearances.
The rampant Blues added a third when captain Terry ran the length of the field to slide home Cesc Fabregas’ low cross.
Viler’s own goal handed the west Londoners a fourth in the second-half before the Slovenians were denied a consolation when Agim Ibraimi hit the post from the penalty spot.
Hazard slotted home from 12-yards following the third penalty of the night 13 minutes from time and the Belgian star completed their biggest ever win in Europe’s elite competition with a sixth a minute before time.
The watching England manager Roy Hodgson would have been impressed, even though Terry’s controversial international career is over, as he watched a number of Slovenia players ahead of next month’s Euro 2016 qualifier.
Mourinho, though, has a right to be concerned ahead of Sunday’s trip to Manchester United as Remy, who started again up front with Diego Costa’s hamstring problem ongoing, scored before going off with an apparent groin problem.
Two of Chelsea’s three front-line strikers are now injured, while the 36-year-old Drogba has only just returned from an ankle problem and is not ready to play 90 minutes.
Chelsea had opened their Group G campaign with a 1-1 draw at home to Schalke, but a 1-0 win at Sporting Lisbon and the thumping of Maribor leaves the Blues in prime position ahead of the November 5 trip to Slovenia.
First up for the Blues, unbeaten this season, is a return to Premier League business at Old Trafford, where Mourinho will come up against his former mentor Louis van Gaal.