Goals from Ross Barkley and Olivier Giroud either side of half time put the Blues in command of the tie, though Anders Christiansen did pull one back 10 minutes from time to give the Swedish side some hope.
Chelsea may be considered the bookmakers' favourites to go all the way and lift the Europa League trophy in Baku three months from now, but it remains to be seen whether Maurizio Sarri will be given the chance to guide them there.
The Italian manager has come under intense pressure in recent weeks following a poor run of results, culminating in Monday's 2-0 loss to Manchester United in round five of the FA Cup.
Despite each of his subs being jeered by supporters, with those in attendance at Stamford Bridge frustrated with Sarri's like-for-like changes, the ex-Napoli boss has a chance to redeem himself somewhat over the coming days.
Victory over Malmo is a must, of course, though three days later comes an even bigger game as the Blues take on Manchester City - the side that thumped them 6-0 earlier this month - in the EFL Cup final.
Sarri insisted before the defeat to United that he has no intention of changing his formation and playing style, though he may well have to have a rethink as his side failed to register a shot on target between the 11th minute and full time of that crushing loss.
Eden Hazard aside, none of Chelsea's players came out of the United defeat with any sort of credit. As well as being caught cold defensively for both goals, the 2018 FA Cup winners also offered next to nothing in an attacking sense when given 45 minutes to find a route back into the game.
With each match seemingly comes more pressure for Sarri, and any sort of slip-up against Malmo in midweek could easily spell the end of his tenure. That would be incredibly cruel on the eve of the EFL Cup final, but this is Chelsea we are talking about.
The Europa League has provided the West Londoners with plenty of smiles this term, however, having cruised through the group stage with 16 points from a possible 18 prior to picking up a first-leg lead against Malmo, so a shock loss on home soil this week seems unthinkable.
Recent form in Europa League: WWWWDW
Recent form (all competitions): WLWLWL
Malmo have already fared a lot better in this season's Europa League compared to their only previous involvement in 2011-12 when collecting just one point in the group stage.
They chalked up a far healthier tally of nine points this time around, losing their opening fixture at Genk but remaining unbeaten over the next five matchdays. Three successive draws, bookended by wins over Besiktas, saw the Swedish side finish second in Group I.
Not a lot was expected of the Sky Blues beyond the group phase, however, as they have not competed in the knockout stages of a European competition since the 1980s when losing to Ajax in the quarter-finals of the European Cup Winners' Cup.
Malmo's aim of prolonging their European adventure into spring took a major hit when losing 2-1 at home in the first leg, as they have been unable to recover on all eight previous occasions that they have been beaten at home in the first leg of a UEFA tie.
The 20-time champions of Sweden are by no means out of the two-legged affair just yet, however, thanks to Christiansen's late strike at the Swedbank Stadium last week.
Uwe Rosler's side have lost just once on their European travels this term, keeping clean sheets in five of those seven fixtures. They were 1-0 winners at Besiktas in their most recent such fixture - Marcus Antonsson scoring the only goal of the game to send the Sky Blues through to the first knockout stage.
Like Chelsea, Malmo have also been in action since the first leg in Sweden, seeing off Degerfors 3-2 in the Svenska Cupen on Sunday - a victory that gave Rosler a chance to get his players back up to speed following the winter break and gain some much-needed momentum.
Malmo's season will not be defined by how far they make it on the continental stage. This will instead be considered a free hit, and after losing the first leg by just a solitary goal the Sky Blues will head to West London in a confident mood.
Recent form in Europa League: WDDDWL
Recent form (all competitions): DWDWLW
This second leg comes at an awkward time for Sarri, sandwiched by cup games against Manchester duo United and City. Changes can therefore be expected, though with the tie still in the balance it will not be a complete overhaul.
Sarri went with Giroud through the middle for the first leg and the Frenchman, having stayed on the bench against Man United, is almost certain to return on Thursday.
Willian, who has created 22 goalscoring chances for Chelsea in the 2018-19 Europa League, scoring two and assisting three goals, is also in line to return to the forward line, as is youngster Callum Hudson-Odoi.
In terms of the visitors, Rosler may stick with the same XI that started the first leg as he has no fresh injury problems to contend with.
Carlos Strandberg and Oscar Lewicki were brought off the bench to offer an attacking threat and are pushing for inclusion here, but Antonsson and Arnor Ingvi Traustason are more likely to be used from the off.
Of the remaining 32 teams in the 2018-19 UEFA Europa League, Malmo have had the oldest starting XI on average in this season's tournament (29y 353d).
Chelsea possible starting lineup:
Kepa; Azpilicueta, Luiz, Christensen, Emerson; Kante, Jorginho, Barkley; Willian, Giroud, Hudson-Odoi
Malmo possible starting lineup:
Dahlin; Nielsen, Bengtsson, Safari; Vindheim, Christiansen, Bachirou, Traustason, Rieks; Rosenberg, Antonsson
Head To Head
Last week's first leg, watched by a full house at the Swedbank Stadion, was the first time that Chelsea and Malmo have met in UEFA competition.
The Blues' two previous ties against opponents from Sweden came in the European Cup Winners' Cup when they were holders of the trophy, being eliminated by Atvidaberg on away goals in 1971-72 but progressing past Helsingborg 17 years later.
Malmo's most famous fixture against English opposition was their first - the 1979 European Champion Clubs' Cup final against Nottingham Forest, which they lost 1-0. Their only win against an English side came 16 years later when they beat Forest in the UEFA Cup.
We say: Chelsea 3-0 Malmo (5-1 on agg)
Chelsea have won each of their last six Europa League home games, scoring at least three goals in five of those matches and netting 17 in total. Swedish sides have won just once in their last seven European away encounters with English teams, meanwhile, so everything points to a much-needed victory for the Blues.