After being frustrated in the first half, the Blues went ahead when Hakim Ziyech converted at the back post following an excellent cross from Callum Hudson-Odoi.
Thiago Silva nearly grabbed a second but his glancing header was cleared off the line by Anel Ahmedhodzic.
It was another masterful defensive display from Thomas Tuchel’s side, who denied Malmo a single shot on target.
Chelsea have nine points from four matches in Group H, the same total as Juventus, who face Zenit St Petersburg at home on Tuesday evening (20:00 GMT).
If the Russians lose in Italy then Chelsea would only need a draw at home to Juventus on 23 November to qualify for the last 16 with a game to spare.
Another strong Chelsea defensive showing
Malmo, managed by ex-Newcastle striker Jon Dahl Tomasson, were playing their 11th match in this season’s competition after battling through four rounds of qualifying, knocking out Rangers on the way.
However, they had suffered heavy losses in their three previous group matches, including a 4-0 defeat by Tuchel’s team at Stamford Bridge in October.
Only the form of home goalkeeper Johan Dahlin denied Chelsea a first-half goal as he kept out efforts, albeit sometimes unconvincingly, from Cesar Azpilicueta, Ziyech, Kai Havertz and Andreas Christensen, while England midfielder Ruben Loftus-Cheek twice narrowly missed the target.
A capacity crowd at the Eleda Stadion produced a fine atmosphere with the home fans trying to inspire their team to their first Champions League point of the season.
Top goalscorer Antonio Colak almost gave the supporters something to cheer about in first-half injury time as he showed great technique to connect with a volley from a long ball forward, but could only steer the shot wide.
Soren Rieks also put a half volley wide early in the second half as the Swedish league leaders threatened to cause a shock.
Loftus-Cheek, lively in only his fifth start of the season, had an effort parried by the erratic Dahlin before Marcos Alonso’s glanced header was blocked.
But Chelsea, just as they had done in their 3-0 win over Newcastle on Saturday, had to be patient before eventually making the breakthrough, which came in the 56th minute.
Hudson-Odoi, on the right wing, played a one-two with Havertz and then produced an exquisite low ball which evaded Ahmedhodzic and Dahlin, with Ziyech putting the ball away at the back post.
Chelsea were again without injured strike-pair Romelu Lukaku and Timo Werner, while Mason Mount had not recovered from an illness that also saw him miss the Newcastle game.
But there was one returning player as United States midfielder Christian Pulisic came on as a second-half substitute for his first club appearance since August after an ankle injury had kept him out for two months.
Another pleasing aspect for Tuchel was yet another impressive performance from his defence as they kept their 10th clean sheet from 17 matches in all competitions.