Ross Barkley and Olivier Giroud scored as Chelsea earned a 2-1 win away to Malmo in the first leg of its Europa League last-32 meeting.
Chelsea had lost its past four straight away games in all competitions without scoring, a run that had its nadir in Sunday's 6-0 humiliation at the hands of Premier League champions Manchester City.
Against more modest opposition at Swedbank Stadion on Thursday, Chelsea took a 2-0 lead thanks to goals either side of the break by Barkley and Giroud.
But although Maurizio Sarri's men appeared to be cruising to a morale-boosting win, Malmo will travel to London with hope after Anders Christiansen's excellent late reply.
Chelsea took the lead with the game's first shot on target after 30 minutes.
Pedro floated in a cross from the right channel and, after defender Lasse Nielsen slipped, Barkley collected the ball and stabbed it past goalkeeper Johan Dahlin.
Arnor Ingvi Traustason fired wide at the end of a goalmouth scramble as a series of set-pieces caused Chelsea problems before the break, but Malmo's wasted openings was punished in the 58th minute.
Brazil winger Willian raided down the left and fed Giroud, who cleverly beat Dahlin with an improvised close-range finish to score in his fourth consecutive European appearance.
Dahlin made a great save to deny Barkley his second of the game but, after the introduction of Eden Hazard as a substitute, Chelsea were caught on the counter.
Christiansen burst on to a perfectly played throughball by Markus Rosenberg and beat Kepa Arrizabalaga with a placed finish to cut the Swedish side's deficit ahead of next week's Stamford Bridge return.
What does it mean? Chelsea stick to same 'Sarriball' style
Suffering a record Premier League defeat would have prompted a tactical rethink from many managers.
But the under-pressure Sarri is unlike most coaches and Chelsea lined up with exactly the same system, although Malmo – playing their first competitive game since the end of the group stage in December – were unable to take full advantage of obvious defensive weaknesses.
Barkley bounces back
Among Chelsea's worst performers at the Etihad Stadium, where his awful headed error gifted Sergio Aguero a simple goal, Barkley produced an improved performance that was capped with a well-taken opener from one of the few clear chances on offer.
Nielsen slip lets Barkley in
A tight first half needed a defensive mistake to give Barkley his chance. Nielsen picked a bad moment to lose his footing and Malmo's composure and competitiveness then ebbed away before a late rally.
- Chelsea has won the opening leg of a European knockout tie for the first time since April 2013 (versus Basel in the Europa League, 2-1) – it was winless in six such matches prior to this victory (D3 L3).
- Malmo has been beaten at home in Europe for the first time since November 2015, ending a run of eight games without defeat in front of its own fans (W2 D6).
- Chelsea has kept just one clean sheet in its last 11 away games in all competitions - it had kept seven clean sheets in the 11 games prior to that.
- Ross Barkley scored Chelsea's first away goal in all competitions in 2019.
- Olivier Giroud is the first Chelsea player to score in four successive games in European competition since Victor Moses in May 2013.
The second leg is a week away, but before that Chelsea host Manchester United in the fifth round of the FA Cup on Monday. Malmo, meanwhile, also have a cup game next with Degerfors the visitors to Swedbank Stadion on Sunday.
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