While the home side were beaten by Olympiacos, their Finnish counterparts fell to a narrow aggregate defeat against Malmo, so the pair will now battle it out for a spot in the playoff round.
Following HJK's crushing 7-1 aggregate victory over Buducnost Podgorica in the first round of Champions League qualification, dreams of a first group stage campaign since the turn of the century started to grow.
Ever since they competed alongside Benfica, PSV, and then Bundesliga champions Kaiserslautern during the 1998-99 season, the Finns have never managed to go further than the third stage of the preliminaries for Europe's top-tier competition - but failed to even get that far this year, after a second-round exit to Nordic neighbours Malmo last week.
Trailing 2-1 from the first leg, HJK went ahead within seconds of the return fixture's start, when Miro Tenho hauled them level at 2-2 on aggregate. However, Malmo skipper Anders Christiansen - who also struck in the first match - and then Veljko Birmancevic struck to end all hopes of an upset, before Roope Riski bagged a late consolation goal.
Including strikes in both legs versus the Swedish champions, 29-year-old Riski - only left out of Finland's Euros squad at the final moment - has led the way in Europe so far. After rattling in five Champions League qualifying goals across four games, he should pose a serious threat to the Neftchi back line on Tuesday, but his team's league form has gone off the boil since returning to continental competition.
Nonetheless, despite recently going down 2-1 away to humble Oulu - who had previously won just one Veikkausliiga game - and recording a goalless draw with SJK at the weekend, Toni Koskela's men remain seven points clear at the top of the table in defence of their domestic title.
Saturday's blank aside, they have established a healthy goal tally in Finland's top flight this term - registering at a rate of nearly two per game - and creating chances in Baku should not be a problem for a multinational squad.
Tuesday's opponents Neftchi, if anything, boast an even more diverse collection of talent than the Helsinki-based club, with Paraguayan, Santomean and Nigerian players all featuring among head coach Samir Abbasov's first-choice selection of late.
The first Azeri team to make the group stage of any UEFA competition back in 2012 - finishing bottom, but picking up memorable points against both Partizan Belgrade and Inter Milan in the Europa League - they have rarely come close to a return since.
Though yet to start the defence of their first league title since 2013, earlier this month, Neftchi came through their first competitive task of the current term by beating Dinamo Tbilisi 2-1 both home and away in the first round of Champions League qualifying.
They had previously posted a pre-season friendly win over Spartak Moscow to bolster a record stretching back to last season reading eight wins from 11 games, before a pair of 1-0 defeats to Greek giants Olympiacos during the past fortnight. With their hopes subsequently switching to Europe's secondary club competition, the ambitious club will expect to get straight back on track this week.
Neftchi have doubts over star striker Namiq Alasgarov's availability on Tuesday, after the former Qarabag man came off in the first game against Olympiacos and subsequently missed the second.
The visitors, meanwhile, could have both Kevin Kouassivi-Benissan and Santeri Vaananen out of action again, while defender Igor Cukovic is also sidelined due to long-term injury. Finland defender Daniel O'Shaughnessy, who started each of his nation's Euro 2020 group games, will therefore helm HJK's four-man defensive unit.
Atomu Tanaka - currently in his second spell at the club - is again poised to link up with chief goal-getter Roope Riski in attack, while the latter's brother Riku Riski is another attacking option alongside young Anthony Olusanya on the bench.
Neftchi Baku possible starting lineup:
Mammadov; Celik, Stankovic, Mbodj, Basque; Harramiz, Kane, Mahmudov, Bougrine, Lawal; Colli
HJK Helsinki possible starting lineup:
Tannander; Moren, Tenho, O'Shaughnessy, Murillo; Saksela, Tavares, Lingman, Valencic; Tanaka, Riski
We say: Neftchi Baku 1-0 HJK Helsinki
While Neftchi have demonstrated their mettle during two closely fought legs with Olympiacos, they are still a little behind HJK in terms of game time at this early stage of the new season.
They are generally tight at the back, though, so the visitors may draw a rare blank in Baku - staying in close enough contention to turn the tie around at home next week.