First-half goals from skipper Jiloan Hamad and Magnus Eriksson, just two minutes apart, ensured the Easter Road team were forced to endure a long evening in the second qualifying round first leg match at Swedbank Stadion.
The visitors face a tough return back in Edinburgh next Thursday against a team whose greater sharpness and fitness from being almost midway through their domestic season was clearly evident.
As predicted 24 hours before by manager Pat Fenlon, Hibs were without Ryan McGivern because of a knee injury and with teenage winger Alex Harris restricted to a place on the bench due to a thigh problem.
With Fraser Mullen, a summer signing from Hearts, deemed not fit enough to start and fellow right-back Tim Clancy out following a close-season groin operation, the Scots' rearguard took on a makeshift look. Lewis Stevenson was called on to plug the right-back gap, with Paul Hanlon moving to the other side of defence and teenager Jordon Forster, who filled in for captain James McPake in the Scottish Cup final in May, continuing his meteoric rise with a European outing.
New signings Liam Craig, Owain Tudur Jones and Rowan Vine were all handed glamour debuts, with the re-signed Kevin Thomson charged with utilising European experience built up in the Champions League and UEFA Cup with Rangers.
Hibs should have been ahead after just seven minutes when Tudur Jones rose unmarked to meet Craig's free-kick - but the summer recruit from Inverness headed wastefully over. And within three minutes, the Scots were behind.
McPake was booked for an apparent tug on striker Tokelo Rantie as the South African international looked to race onto a throughball and Hamad sent his 20-yard free-kick into the net via the underside of the crossbar.
Within two minutes, the costly start was complete as Malmo doubled their lead. Emil Forsberg created space on the left side of the penalty box and his cutback was slotted home by Eriksson.
In the end, after repelling everything Malmo could throw at them in the second half, Hibs will have been delighted to get to the full-time whistle with just a two-goal deficit to chase next week back in Scotland.
However, St Johnstone pulled off a shock 1-0 win in their Europa League second qualifying round first leg match in Norway, as defender Frazer Wright's first-half goal stunned Rosenborg.
The centre-half made the most of a brief period of Saints pressure in the opening stages to net from close range and secure his side a precious away goal.
But there were worrying moments following Wright's 19th-minute strike and Tommy Wright's team were forced to defend stoutly to protect their lead.
The Perth side's goalkeeper Alan Mannus in particular did his best to ensure the clean-sheet was guarded as he pulled off a string of important saves in the minutes following the start of the second-half.
St Johnstone will now hope to complete a remarkable victory when they host the 22-time Norwegian champions in the return leg at McDiarmid Park next Thursday.
Saints started in Trondheim with two of their five summer signings as former Hamilton midfielder Gary McDonald joined ex-Hibernian player David Wotherspoon in their five-man midfield.
Aaron Burns' strike secured Linfield a famous Europa League win against Xanthi.
Burns grabbed the winner in the 25th minute, firing past Christian Gimenez after good work down the left.
Xanthi enjoyed the lion's share of possession after the goal, but Belfast-outfit Linfield held on to take a 1-0 lead into next week's second leg at Windsor Park.
Derry were another side to impress in Europe as they gave Trabzonspor a scare.
Adrian Mierzejewski and Paulo Henrique efforts gave the Turkish side a two-goal lead within 16 minutes, only for City to come storming back.
David McDaid pulled one back at the Huseyin Avni Aker Stadium, before Patrick Kavanagh drew parity in the 32nd minute.
It had looked like another shock could be on the cards, only for an own goal from captain Barry Molloy to put Derry on the back foot before half-time.
Giray Kacar put Trabzonspor further ahead early in the second half but City continued to threaten, with Ryan McBride firing just wide in injury time as the match finished 4-2 to the hosts.
Prestatyn Town's task next week looks nigh on impossible after suffering a 5-0 hammering in Croatia.
Rijeka came into the match as overwhelming favourites and did not disappoint, with former international Leon Benko netting a hat-trick before Vedran Jugovic and Damir Zlomislic added gloss to the scoreline.
Breidablik (Iceland) - Sturm Graz (Austria) 0-0 (halftime: 0-0)
KR (Iceland) - Standard Liege (Belgium) 1-3 (halftime: 1-1)
Rijeka (Croatia) - Prestatyn Town (Wales) 5-0 (halftime: 2-0)
Olimpija Ljubljana (Slovenia) - Zilina (Slovakia) 3-1 (halftime: 2-0)
Slask Wroclaw (Poland) - Rudar (Montenegro) 4-0 (halftime: 2-0)
Red Star Belgrade (Serbia) - IBV (Iceland) 2-0 (halftime: 1-0)
FC Astra (Romania) - Omonia Nicosia (Cyprus) 1-1 (halftime: 1-0)
Hajduk Split (Croatia) - FK Turnovo (Macedonia FYR) 2-1 (halftime: 1-1)
Trabzonspor (Turkey) - Derry City (Ireland) 4-2 (halftime: 3-2)
Vojvodina Novi Sad (Serbia) - Honved (Hungary) 2-0 (halftime: 1-0)
Sparta Prague (Czech Republic) - Haecken (Sweden) 2-2 (halftime: 1-0)
Xanthi (Greece) - Linfield (Northern Ireland) 0-1 (halftime: 0-1)
Zalgiris Vilnius (Lithuania) - Pyunik Yerevan (Armenia) 2-0 (halftime: 0-0)
Jagodina (Serbia) - Rubin Kazan (Russia) 2-3 (halftime: 0-2)
FC Differdange 03 (Luxembourg) - Utrecht (Netherlands) 2-1 (halftime: 1-1)
Thun (Switzerland) - Chikhura Sachkere (Georgia) 2-0 (halftime: 2-0)
Kukesi (Albania) - Sarajevo (Bosnia & Herzegovina) 3-2 (halftime: 2-2)
Valletta FC (Malta) - FK Minsk (Belarus) 1-1 (halftime: 1-1)
Anorthosis Famagusta (Cyprus) - Gefle (Sweden) 3-0 (halftime: 2-0)
Chernomorets Odessa (Ukraine) - Dacia Chisinau (Moldova) 2-0 (halftime: 0-0)
IFK Gothenburg (Sweden) - Laugaricio Trencin (Slovakia) 0-0 (halftime: 0-0)
IL Hodd (Norway) (II) - FK Aktobe (Kazakhstan) 1-0 (halftime: 1-0)
Maccabi Haifa (Israel) - Khazar Lenkoran (Azerbaijan) 2-0 (halftime: 1-0)
Malmo (Sweden) - Hibernian (Scotland) 2-0 (halftime: 2-0)
Petrolul Ploiesti (Romania) - Vikingur (Faroe Islands) 3-0 (halftime: 1-0)
Rosenborg Trondheim (Norway) - St. Johnstone (Scotland) 0-1 (halftime: 0-1)
Stromsgodset IF (Norway) - Debrecen (Hungary) 2-2 (halftime: 0-1)
Tromso (Norway) - Inter Baku (Azerbaijan) 2-0 (halftime: 1-0)
Beroe Stara Zagora (Bulgaria) - Hapoel Tel Aviv (Israel) 1-4 (halftime: 1-2)
Zrinjski (Bosnia & Herzegovina) - Botev Plovdiv (Bulgaria) 1-1 (halftime: 1-0)
Skonto FC (Latvia) - Slovan Liberec (Czech Republic) 2-1 (halftime: 1-1)
Dinamo Minsk (Belarus) - Lokomotiva Zagreb (Croatia) 1-2 (halftime: 0-2)
FC Honka (Finland) - Lech Poznan (Poland) 1-3 (halftime: 1-1)
Garabagh Agdam (Azerbaijan) - Piast Gliwice (Poland) 2-1 (halftime: 1-1)
Shakhter Soligorsk (Belarus) - Milsami Orhei (Moldova) 1-1 (halftime: 1-0)
Mladost (Montenegro) - FK Senica (Slovakia) 2-2 (halftime: 0-1)
FK Ventspils (Latvia) - Jeunesse Esch (Luxembourg) 1-0 (halftime: 1-0)
Dila Gori (Georgia) - AaB Aalborg (Denmark) 3-0 (halftime: 0-0)
Irtysh Pavlodar (Kazakhstan) - Siroki Brijeg (Bosnia & Herzegovina) 3-2 (halftime: 2-0)
- Sports & Recreation