A place in the draw for the first round proper will be at stake for Rovers and the Pars.
Mark Hughes' Blackburn side reached this stage of the competition by beating Lithuanian side FK Vetra 6-0 on aggregate in the Intertoto Cup.
MyPa are fourth in their domestic top flight and have conquered Motherwell and Dundee United in past European campaigns.
Tennent's Scottish Cup runners-up Dunfermline, preparing for life outside the Scottish top flight, will be off to Gothenburg for their tie. Like the Pars, BK Hacken were also relegated at the end of their previous domestic campaign.
Irish Eircom League side Drogheda's reward for beating San Marino side Libertas in the first qualifying round is a tie against Swedish club Helsingborgs, where former Celtic, Barcelona and Manchester United star Henrik Larsson plays his football.
The ties will be played on August 16 and 30.
Draw for second qualifying round of UEFA Cup:
FC Otelul Galati v Lokomotiv Sofia
CFR 1907 Cluj v Anorthosis
FK Rabotnicki v NK Zrinjski or Partizan Belgrade
NK Slaven Koprivnica v Galatasaray
UD Leiria v Maccabi Netanya
Hajduk Split v Sampdoria
KS Besa v Litex Lovech
Maccabi Tel-Aviv v Kayseri Erciyesspor
Atletico Madrid v FK Vojvodina
Siroki Brijeg v Hapoel Tel-Aviv
AC Omonia v CSKA Sofia
Basle v Mattersburg
SV Ried v FC Sion
Mika v Artmedia Bratislava
Dnipro v GKS Belchatow
Budapest Honved v Hamburg
Young Boys v Lens
Tobol Kostanay v Groclin
Austria Vienna v FK Jablonec
Vion Zlate Moravce v Zenit St Petersburg
Rapid Vienna v Dinamo Tbilisi
MyPa v Blackburn
Drogheda United v Helsingborg
Liepajax Metalurgs v AIK Solna
HJK Helsinki v Aalborg
FK Ekranas v Valerenga
Dunfermline v Hacken
Brann v Suduva
Haka v Midtjylland
Dinamo Minsk v Odense
UN Kaerjeng v Standard Liege