Dublin side St Pat's beat IBV of Iceland 1-0 at their Richmond Park ground with Christy Fagan getting the only goal in the 38th minute.
Belfast outfit Cliftonville won by the same scoreline at home as they upset Swedish side Kalmar for what was their first ever home victory in Europe.
Substitute Liam Boyce scored the famous goal just seconds after coming on in the 71st minute.
Dublin's Bohemians also faced Icelandic opponents but could only manage a 0-0 draw against Thor Akureyri.
Welsh club Banger City also had a 0-0 home draw in the first leg of their clash with Moldova's Zimbru Chisinau and CEFN Druids AFC produced the same result against MyPa Myllykoski of Finland
It was a tough night for Northern Ireland side Crusaders who could not match Cliftonville's efforts, as they were beaten at home 3-0 by former Norwegian champions Rosenborg.
Welsh side Llanelli lost 2-1 in Finland against KuPS but their away goal will give them hope ahead of next week's second legs.
Results from the UEFA Europa League qualification round one, first leg matches:
FH (Iceland) - USV Eschen-Mauren (Liechtenstein) 2-1 (half-time: 1-0)
Borac Banja Luka (Bosnia & Herzegovina) - Celik (Montenegro) 2-2 (half-time: 2-1)
Crusaders (Northern Ireland) – Rosenborg Trondheim (Norway) 0-3 (half-time: 0-1)
Bangor City (Wales) - Zimbru Chisinau (Moldova) 0-0 (half-time: 0-0)
Bohemians (Ireland) - Thor Akureyri (Iceland) 0-0 (half-time: 0-0)
Cliftonville (Northern Ireland) - Kalmar (Sweden) 1-0 (half-time: 0-0)
St. Patrick's Athletic (Ireland) - IBV (Iceland) 1-0 (half-time: 1-0)
CEFN Druids AFC (Wales) - MyPa Myllykoski (Finland) 0-0 (half-time: 0-0)
Flamurtari (Albania) - Honved (Hungary) 0-1 (half-time: 0-0)
La Fiorita (San Marino) - SK Liepajas Metalurgs (Latvia) 0-2 (half-time: 0-1)
Teuta Durrës (Albania) - FC Rustavi Metalurgist (Georgia) 0-3 (half-time: 0-0)
MTK Hungaria (Hungary) - FK Senica (Slovakia) 1-1 (half-time: 1-0)
EB/Streymur (Faroe Islands) - Gandzasar Kapan (Armenia) 3-1 (half-time: 3-0)
Lech Poznan (Poland) – Zhetisu Taldyqorghan (Kazakhstan) 2-0 (half-time: 0-0)
Olimpija Ljubljana (Slovenia) - Jeunesse Esch (Luxembourg) 3-0 (half-time: 0-0)
Twente Enschede (Netherlands) - UE Santa Coloma (Andorra) 6-0 (half-time: 2-0)
FC Santa Coloma (Andorra) - Osijek (Croatia) 0-1 (half-time: 0-0)
Sarajevo (Bosnia & Herzegovina) - Hibernians (Malta) 5-2 (half-time: 2-2)
Birkirkara (Malta) - Metalurg Skopje (Macedonia FYR) 2-2 (half-time: 0-1)
SK Tirane (Albania) - CS Grevenmacher (Luxembourg) 2-0 (half-time: 2-0)
Torpedo Kutaisi (Georgia) - FK Aktobe (Kazakhstan) 1-1 (half-time: 0-0)
Dacia Chisinau (Moldova) - MIK Celje (Slovenia) 1-0 (half-time: 1-0)
FC Differdange 03 (Luxembourg) - NSI Runavik (Faroe Islands) 3-0 (half-time: 2-0)
Suduva Marijampole (Lithuania) - Daugava Daugavpils (Latvia) 0-1 (half-time: 0-0)
FK Baki (Azerbaijan) - Mura 05 (Slovenia) 0-0 (half-time: 0-0)
Elfsborg Boras (Sweden) - Floriana (Malta) 8-0 (half-time: 5-0)
JJK (Finland) - Stabaek (Norway) 2-0 (half-time: 1-0)
Pyunik Yerevan (Armenia) - Zeta Golubovci (Montenegro) 0-3 (half-time: 0-0)
Rudar (Montenegro) - Shirak Gyumri (Armenia) 0-1 (half-time: 0-0)
FC Levadia Tallinn (Estonia) - KFK Siauliai (Lithuania) 1-0 (half-time: 0-0)
Jagodina (Serbia) – Ordabasy (Kazakhstan) 0-1 (half-time: 0-0)
KuPS (Finland) - Llanelli (Wales) 2-1 (half-time: 2-1)
Renova Cepciste (Macedonia FYR) - Libertas (San Marino) 4-0 (half-time: 2-0)
Trans Narva (Estonia) - Inter Baku (Azerbaijan) 0-5 (half-time: 0-2)
Khazar Lenkoran (Azerbaijan) - Kalju Nomme (Estonia) 2-2 (half-time: 2-1)
Shkendija 79 (Macedonia FYR) – Portadown (Northern Ireland) 0-0 (half-time: 0-0)
Víkingur (Faroe Islands) - FK Gomel (Belarus) 0-6 (half-time: 0-0)