Hakim Ziyech scored his first Chelsea goal as Frank Lampard's side picked up three points in an emphatic Champions League win in Russia.
Ziyech, 27, swept in on his first start for the club to add to goals from Callum Hudson-Odoi, Timo Werner and Christian Pulisic as Chelsea returned to goalscoring ways in style.
Back-to-back goalless draws had signalled that Lampard had made strides in sorting out his side's defence, and while they will face tougher opposition than Russian new boys Krasnodar, the manager will be delighted that his attacking riches also kicked into gear after midfielder Jorginho had missed an early penalty.
Four points from two games is a solid start to their Champions League campaign and despite their run of draws Chelsea have now lost just once in 10 games this term.
Blues back on target
Lampard has undertaken a rebuild of his side and could field around £160m of new attacking talent as Ziyech joined Werner and Kai Havertz in the starting XI.
But, initially at least, the visitors were still guilty of moving the ball too slowly against some spirited and organised opponents.
Werner was lively if underused, and won the early penalty when he was tripped by Kaio. Jorginho stuck with his usual skipping technique, sent goalkeeper Matvey Safonov the wrong way, but hit the base of the post.
Chelsea needed a helping hand to end their 248-minute goal drought and duly got one from Safonov when the 21-year-old goalkeeper made a total hash of dealing with Hudson-Odoi's scuffed shot, the ball bobbling in.
Lampard's side were always comfortable but had to endure a sticky spell when Yuri Gazinsky hit the crossbar from a corner. A second penalty, harshly given for handball, was then thrashed home by Werner to shut down any signs of a fightback.
Ziyech, who showed encouraging signs throughout and who should have scored earlier after a great turn, found the bottom corner after good approach play from substitute Pulisic, and the American made it four in the last minute when he drove past Safonov.
Tammy Abraham's assist for the fourth, and the fact Olivier Giroud remained on the bench, only served to underline the fact that goals should not be an issue for this Chelsea team.
New pin in the CL map
Chelsea fans have had to endure derogatory, baseless chants down the years from rival fans claiming that they have "no history".
If any away fans had been allowed into the UFO-like Krasnodar Stadium, which was raucous throughout as a crowd of around 11,000 made themselves heard, they could have legitimately returned fire.
Krasnodar were only formed in 2008, just a few months before Chelsea lost the Champions League final on Russian soil. Lampard himself had already played 400 games before Chelsea's 55th Champions League opponents were forged by a supermarket magnate.
Krasnodar may lack in household names but had Chelsea worried for a spell in the second half, particularly when the excellent Edouard Mendy was beaten by Gazinsky, the midfielder's shot hitting the crossbar.
The second penalty killed off their challenge though as Chelsea romped to their biggest Champions League victory since a 4-0 win over FK Qarabag in November 2017.
Follow reaction and the latest from Wednesday's late games
Chelsea are unbeaten in their last eight group stage away games in European competition (W6 D2), keeping a clean sheet in five of those matches in this run.
Chelsea have kept successive clean sheets in the Champions League for the first time since December 2015, and in their opening two group stage games of a CL campaign for the first time since 2008-09.
Chelsea have kept three clean sheets in a row in all competitions for the very first time under Frank Lampard, also recording shutouts for the first time in successive away games under the former Chelsea midfielder.
Chelsea's Kai Havertz has been involved in seven goals in his last seven games in European competition (4 goals, 3 assists), with his assist against FK Krasnodar his first goal involvement in the Champions League (10th appearance).
Callum Hudson-Odoi is just the second teenager to score for Chelsea in the Champions League, alongside Reece James, who did so against Ajax last season.
Chelsea's Hakim Ziyech has been directly involved in 13 goals in his last 15 starts in the Champions League, scoring six goals and assisting a further seven.
All eight of Chelsea forward Timo Werner's Champions League goals have come away from home - he's the top scorer in the competition to have scored 100% of their goals on the road.