While the visitors came out on top in an enthralling tussle with Vikingur - winning 6-5 on aggregate - it took their hosts an intense period of extra time to see off Kosovan champions KF Ballkani.
Match preview
Having traded goals in the opening half-hour of their first leg, Zalgiris and Ballkani then went over two hours of football without either side finding a decisive goal in their first round tie.
Eventually, though, the A Lyga champions managed to steal a place in the next stage of Champions League qualifying, as Nigerian striker Mathias Oyewusi struck in the seventh minute of extra time at LFF Stadium.
Zalgiris are now targeting a first-ever group stage qualification, having won the Lithuanian league title for the ninth time last season, and hope to fare better than their attempt this time last year.
The Vilnius outfit were eliminated in the second qualifying round, before losing in the third round of the Europa League preliminaries and then to Bodo/Glimt in the playoffs for entry to the inaugural Europa Conference League.
Twelve months on, in defence of their domestic crown, Vladimir Cheburin's side have racked up 41 points from 18 league games to sit top of the table by two points, with two games in hand.
Their most recent fixtures have been postponed, to allow them to concentrate on European engagements, but Cheburin had steered his team to four straight A Lyga wins before the meeting with Ballkani. In the Champions League, however, Zalgiris are owners of a past record that includes 11 defeats and just six wins from 20 matches.
Malmo, meanwhile, reconvened with Vikingur for the away leg of their first round tie last Tuesday, following an explosive encounter back in Sweden.
The Allsvenskan champions led 3-2 from their first leg clash at Eleda Stadion, having struggled to see off 10-man opponents, and a similarly open contest was in store at Reykjavik's Vikingsvollur.
After opening up a three-goal advantage through first-half strikes from Veljko Birmancevic, Felix Beijmo and captain Anders Christiansen, Malmo allowed their hosts to sneak back into contention, before holding on for a 3-3 draw on the night.
Milos Milojevic's side then returned to playing catch-up in the defence of their domestic title, and they are within three points of the Allsvenskan summit following Saturday's 2-0 win at Norkopping.
It has not been plain sailing since Milojevic took the reins from former coach Jon Dahl Tomasson, who led the club to successive league titles and last year's Champions League group stage before departing for Championship side Blackburn Rovers.
Di Blae seem to be running into some hot goalscoring form, though, and having netted at least twice in six of their last seven competitive matches they will be confident of taking a lead back home on Tuesday.
FK Zalgiris Champions League form:
FK Zalgiris form (all competitions):
Malmo Champions League form:
Malmo form (all competitions):
Team News
Zalgiris are likely to replicate the 4-4-2 setup they deployed in the previous round, with Swiss midfielder Oliver Buff given license to link up with the hosts' front two.
There is strong competition for the strikers' spots in Vladimir Cheburin's first XI, and Renan Oliveira is set to continue alongside either Josip Tadic, Marko Milickovic or last week's hero Mathias Oyewusi.
The former has scored eight times in 13 appearances for the club since signing on loan from Ukraine's Kolos Kovalivka, having also spent time in Slovakia and Malta.
Meanwhile, Malmo's new acquisitions Moustafa Zeidan and Mahame Siby both made promising debuts on Saturday, forming a new three-man midfield alongside Peru's Sergio Pena against Norkopping.
Though captain Andreas Christiansen was rested at the weekend, the Denmark international is likely to be brought back in for Champions League duty, but speedy winger Joseph Ceesay - signed from Lechia Gdansk earlier this month - could retain his place.
Both mainstays of the visitors' recent successes, Anel Ahmedhodzic and Croatian striker Antonio Colak have moved to British clubs over the past few days, while Soren Rieks, Oscar Lewicki and Adi Nalic are all sidelined by injury.
In Colak's absence, Isaac Kiese Thelin and Veljko Birmancevic will carry the can up front - the latter has posted three goals and as many assists from 13 Allsvenskan appearances this season.
FK Zalgiris possible starting lineup:
Gertmonas; Mikoliunas, Pavelic, Ljubisavljevic, Mamic; Kyeremeh, Gorobsov, Buff, Ourega; Oliveira, Milickovic
Malmo possible starting lineup:
Dahlin; Beijmo, Hadzikadunic, Moisander, Olsson; Christiansen, Pena; Ceesay, Zeidan, Birmancevic; Thelin
We say: FK Zalgiris 1-2 Malmo
Despite losing Antonio Colak to Rangers, there is no doubt Malmo still pack a punch in the final third, and they are capable of scoring more than once in Vilnius.
Though in good form, Zalgiris may be found out at this stage of qualifying, with their latest visitors - group stage participants last term - representing a significant step up in class.