Whichever side progresses from the third round will meet Serbia's FK Backa Topola in the playoffs later this month.
Match preview
After a first-leg clash that took place in Vilnius rather than Panevezys' more modest Aukstaitija Stadium, Maccabi Tel Aviv left Lithuania with a 2-1 first-leg lead, setting themselves on the road to victory as early as the third minute.
Dor Peretz struck first, before Dor Turgeman soon added another to put Zarko Lazetic's side in control; however, substitute Sivert Gussias replied in the 70th minute and kept the home team in the contest.
Maccabi have experienced a mixed start to their 2024-25 campaign, as after beating Maccabi Petah Tikva to win last month's Israel Super Cup they then exited the Champions League qualifiers at the hands of Romania's FCSB.
As a result, the Tel Aviv club turned their focus to Europa League qualifying, having made the knockout stage of last term's Conference League under former boss Robbie Keane.
Current coach Lazetic can now set up a meeting with his old side Backa Topola in the playoffs, though Maccabi must hold their UEFA 'home' games in Hungary this year, given ongoing conflict in the Middle East.
While Thursday's hosts occasionally appear in European group stages, Panevezys are competing in the qualifiers for just a fourth time, having been established in their current incarnation less than a decade ago.
This year, Stijn Vreven's side claimed a 4-1 aggregate victory over HJK in the Champions League's first qualifying round, before being beaten by Jagiellonia Bialystok and suffering demotion to UEFA's second-tier tournament.
Nonetheless, a club formed from the ashes of seven-time Lithuanian champions FK Ekranas are still just two steps away from making their debut in the group phase.
That would guarantee at least eight high-profile matches in the Europa League's new format, and even losing out to Maccabi Tel Aviv will result in a shot at the Conference League playoffs.
Following Sunday's 0-0 draw with Zalgiris, though, Panevezys occupy last place in the 10-team A Lyga this season, with the reigning champions enduring a dismal defence of their title.
Maccabi Tel Aviv Europa League form:
W
Maccabi Tel Aviv form (all competitions):
Panevezys Europa League form:
L
Panevezys form (all competitions):
D
W
D
L
L
L
Team News
Most of Maccabi Tel Aviv's team should remain unchanged in Hungary, as they have had a full week's rest prior to starting their Israeli Premier League defence; however, Dutch defender Tyrese Asante must serve a suspension for accumulated bookings.
Joris van Overeem, Gabi Kanichowsky and Dor Peretz are set to man the engine room, while forwards Sagiv Jehezkel and Hisham Layous - who both made their first start for the club last week - may again start on either side of Dor Turgeman, albeit Eran Zahavi is waiting in the wings.
Turgeman recently returned from international duty at the Olympics, and his fellow Israel internationals Roy Revivo, Osher Davida, Ido Shahar and Elad Madmon could be named amongst the substitutes; new signing Issouf Sissokho should join them.
Meanwhile, Panevezys boss Stijn Vreven may be tempted to freshen up a side that have been far busier than Maccabi so far this summer.
After scoring in the first leg and then being promoted to the league lineup on Sunday, Norwegian forward Sivert Gussias is pushing hard for a start ahead of former Gillingham striker Noel Mbo.
Maccabi Tel Aviv possible starting lineup:
Mishipati; Nachmias, Shlomo, Bitton, Davidzada; Peretz, Van Overeem, Kanichowsky; Zahavi, Turgeman, Layous
Panevezys possible starting lineup:
Cerniauskas; Rasimavicius, Dubra, Klimavicius, Mazan; Cadjenovic, Gorobsov; Sarpong, De Vega, Dieng; Gussias