It was too easy for the European champions, who will surely expect another three points when they go to Sweden next month for the return fixture.
Perhaps then Tuchel will name a much-changed side to the one he sent out here, which smacked of a manager refusing to take any risks even against such limited opposition.
Defeat to Juventus last time out meant Chelsea could not afford any mis-step in back-to-back games against the Swedish champions, if they are to have any chance of topping Group H and there was no danger of that from the moment Andreas Christensen fired them ahead after nine minutes.
In the end a 4-0 score-line flattered the visitors. This could have been anything – and if not for first half injuries to Romelu Lukaku and Timo Werner, perhaps the margin of victory would have been even greater.
The loss of the two forwards could well be the biggest takeaway from this game, with Chelsea now having to assess both players ahead of Saturday’s game against Norwich.
Lukaku looked in a lot of discomfort as he limped off the pitch with a twisted ankle, while Werner was left clutching his hamstring after pulling up sharply.
At least Kai Havertz was back among the goals – coming on for Lukaku in the first half and finding the back of the net after the break with a smart finish. The German has been warned he faces a fight to force his way back into Tuchel’s first team plans – but fate may have just handed him his chance. Should Lukaku fail to recover in time for the weekend then Havertz is sure to lead Chelsea’s attack.
The decision to play Lukaku was a peculiar one from Tuchel, having claimed the Belgian was physically and mentally tired, as well as complaing about the strain being placed on modern-day players. Yet here he was starting his 11th game of the season, and his ninth from a possible 10 since joining Chelsea in the summer.
There was a sense that Tuchel was hoping the £97.5million striker would play his way back into form after going six games without a goal, his longest barren run since his final season at Manchester United.
This was as bright as he has looked in some time for Chelsea, until his evening was cut short when he went down under the challenge of Lasse Nielsen in the box, twisting his ankle in the process.
Referee Francois Letexier pointed to the spot and Jorginho stepped up to convert to put Chelsea 2-0 up after 20 minutes but Lukaku hobbled to the touchline to be replaced by Havertz before the restart.
He had also been involved in the opening goal, when his deflected effort was pushed away for a corner by Johan Dahlin.
From the set piece Malmo failed to clear the danger, with Thiago Silva picking up the ball on the right. His cross found the run of Christensen, who volleyed home before the clock had reached 10 minutes.
Havertz had the chance to make it 3-0 before the break when slid in by N’Golo Kante - but his shot on the angle was pushed wide by Dahlin. Replays suggested he should have done better.
Even without the cushion of a third, the outcome was never in doubt. Of greater concern was Chelsea’s depleting numbers when Werner was forced off with a pulled hamstring.
Malmo sent on reserve goalkeeper Ismael Diawara after half time – along with Malik Abubukari. They might have been better off loading up with as many keepers as they could as Chelsea kept pouring forward.
Havertz made up for his earlier miss immediately after the restart after a sharp counter attack. Malmo were in the rare position of pressing high up the pitch when substitute Callum Hudson-Odoi broke from his own half. Havertz was with him all the way and was eventually released on the left of the box. The German then lifted a shot over Diawara that went in off the post.
Chelsea won their second penalty with just 10 minutes of the second half played when Eric Larsson bundled into Toni Rudiger, following Havertz’ pass. Jorginho stepped up again and struck his second of the night. Different keeper, same outcome. 4-0.
The only surprise was that Chelsea did not further add to their lead.