Bratislava's pressure eventually told in the latter stages, scoring twice in the final 20 minutes, and the Slovakian outfit are now the big favourites to progress to the next round of the competition on Tuesday night.
Match preview
APOEL are 29-time Cypriot champions, which is a record, and they finished at the top of the pile last season to secure qualification for the Champions League second qualifying round.
David Gallego's side managed to squeeze past Petrocub 2-1 on aggregate in the last round, but they suffered a 2-0 defeat to Bratislava in the first leg of their third qualifying round fixture on August 7.
APOEL famously reached the quarter-finals of the 2011-12 Champions League, which represents their best-ever performance in the European competition, while they were last present in the group stage of Europe's leading cup competition back in 2014-15.
Τhrylos will begin their domestic campaign on August 23, so their full focus is on the Champions League, but they will need to put in a special performance to turn the tie around, as an own goal from Radosav Petrovic sent Bratislava on their way in the first leg, before Robert Mak added a second in the final exchanges.
The visitors also won their domestic title last season, triumphing in the Slovak First Football League for the 22nd time in their history, which saw them enter the Champions League in the first qualifying round.
Vladimir Weiss's side therefore started their European campaign on July 10, beating Strega 4-2 at home and 2-1 away in order to progress to the second qualifying round with an aggregate score of 6-3.
Bratislava were also comfortable in the last round, beating Celje 6-1 on aggregate, and as mentioned, they will bring a 2-0 advantage into the second leg of their third qualifying round clash with APOEL.
The Sky Blues are also two matches into their domestic season, recording two wins to sit at the top of the table, so the visitors will enter this game off the back of four straight victories in all competitions.
Bratislava have never qualified for the group stage of a Champions League, but they famously won the UEFA Cup Winners' Cup in 1969, beating Barcelona in the process, and the team have played in the group stage of the Europa League on three occasions.
APOEL Champions League form:
Slovan Bratislava Champions League form:
Slovan Bratislava form (all competitions):
Team News
APOEL head coach Gallego is expected to resist the temptation to shuffle his pack for this match, and it would not be a shock to see the same XI take to the field from the first leg.
Youssef El-Arabi is perhaps the player pushing strongest to be introduced into the side, but Stefan Drazic is expected to again be given the nod as the centre-forward on Tuesday night.
Marquinhos is another certain starter for the home side, with the 27-year-old already scoring twice in three appearances in the qualification rounds of the Champions League this season.
As for Bratislava, the club have not reported any fitness concerns ahead of Tuesday's second leg.
Mak and David Strelec have both scored four times in six appearances at the start of the new season, and the former is set to be introduced into the side after coming off the bench in the first leg.
Tigran Barseghyan could be the player to miss out despite scoring twice this season, with Vladimir Weiss set to operate alongside Mak and Strelec in the final third of the field.
There will also be a notable inclusion at the back in the shape of 37-year-old Guram Kashia, who helped Georgia reach the last-16 stage of this summer's European Championship.
APOEL possible starting lineup:
Belec; Susic, Petrovic, Dvali, Quintilla; Meyer, Kostadinov, Tejera; Ndongala, Drazic, Marquinhos
Slovan Bratislava possible starting lineup:
Takac; Blackman, Kashia, Wimmer, Zubers; Kucka, Bajric, Polic; Weiss, Strelec, Mak
We say: APOEL 2-2 Slovan Bratislava (Slovan Bratislava win 4-2 on aggregate)
APOEL will have home advantage on Tuesday, which counts for a lot, but we are finding it very difficult to imagine this tie being turned around. Both teams have quality in the final third of the field, and we are expecting an entertaining draw, with Bratislava progressing to the playoff round of the Champions League.