CSKA Sofia defeated Macedonian side Makedonija Gjorce Petrov to reach this stage, while St Patrick's stunned Slovenian side NS Mura.
Match preview
After a drab 0-0 in the first leg in Macedonia, CSKA Sofia demonstrated their superiority over their opponents by thrashing them 4-0 at Bulgarian Army Stadium.
Star striker Georgi Yomov settled any nerves with a fine strike moments after the hour mark to double his side's lead, with Sasa Ilic's side enjoying themselves thereafter with a couple of late goals adding gloss to their victory.
CSKA Sofia were a force on the European stage in previous decades, reaching the semi-final of the European Cup in 1982, as well as the quarter-finals in 1981 and 1990.
However, The Reds cannot even dominate domestically anymore, with rivals Ludogorets Razgrad scooping 11 successive Bulgarian titles since their promotion in 2011.
Should CSKA Sofia manage to progress past St Patrick's and into the Europa Conference League group stage, they will hope for a much better showing than last season, when they gained only one point from six matches.
The Bulgarians would be foolish to underestimate the League of Ireland runners-up, though, given that they have already dumped out a side which reached last season's group stage in this competition.
Indeed, Mura stunned the world by beating Premier League outfit Tottenham Hotspur last season, but the Slovenians could not find their way past St Patrick's across two legs, with penalties ultimately helping Tim Clancy's side progress.
The Athletic have not competed beyond the qualification rounds of any European competition since losing to Hertha Berlin in the first round of the UEFA Cup in 2008, so they are on the brink of making history.
In Bulgaria on Thursday, Clancy will be hoping for a similarly stubborn performance to the one which earned his side a penalty shoot-out after a 0-0 draw in Slovenia, before taking their opponents back to Richmond Park in Dublin next week.
CSKA Sofia Europa Conference League form:
CSKA Sofia form (all competitions):
St Patrick's Athletic Europa Conference League form:
St Patrick's Athletic form (all competitions):
Team News
CSKA Sofia will continue to be without winger Ivan Mitrev, who continues his recovery from a fractured leg.
Ilic is unlikely to make any changes from the XI which thrashed Makedonija last week.
St Patrick's, meanwhile, do not appear to have any injury concerns, so Doyle will take a full squad to select from.
Former Bolton Wanderers forward Eoin Doyle played the full 90 minutes in Slovenia and will be expected to do the same in Bulgaria on Thursday.
CSKA Sofia possible starting lineup:
Busatto; Turitsov, Koch, Mattheij, Minkhov; Youga, Baurenski, Tufegdzic; Yomov, Krastev, Garcez
St Patrick's Athletic possible starting lineup:
Anang; Cotter, Brockbank, Grivotsi, Redmond, Breslin; King, Lennon, O'Reilly, Forrester; Doyle
We say: CSKA Sofia 2-0 St Patrick's Athletic
CSKA Sofia's technical ability is on another level to St Patrick's, and we expect the Bulgarians to secure a comfortable victory.
However, the Irish side have enough about them to dig in and give themselves a glimmer of hope in the return leg.