Trailing 4-0 from the first leg, it was a near impossible task to get anything in Serbia and the Welsh side were 3-0 down after 20 minutes thanks to goals by Lamina Diarra, Cleverson and Nenad Djordjevic.
Brana Ilic made it four seven minutes before the break and Cleverson got his second five minutes after the second-half restart.
Ilic completed his brace 10 minutes later, Radosav Petrovic made it 7-0 on 66 minutes and Brazilian Cleverson sealed his hat-trick from the spot with 18 minutes remaining.
In the other second-round ties, Stabaek, Dinamo Zagreb, Slovan Bratislava, APOEL Nicosia, Sheriff Tiraspol, Levski Sofia, BATE Borisov and FK Baki all went through.
Second-round qualifying results:
Partizan Belgrade (Serbia) 8-0 Rhyl (Wales); Partizan Belgrade win 12-0 on aggregate.
Stabaek (Norway) 4-0 SK Tirane (Albania); Stabaek win 5-1 on aggregate.
Dinamo Zagreb (Croatia) 3-0 Pyunik Yerevan (Armenia); Dinamo Zagreb win 3-0 on aggregate.
Slovan Bratislava (Slovakia) 4-0 Zrinjski (Bosnia & Herzegovina); Slovan Bratislava win 4-1 on aggregate.
APOEL Nicosia (Cyprus) 3-0 EB/Streymur (Faroe Islands); APOEL Nicosia win 5-0 on aggregate.
Sheriff Tiraspol (Moldova) 1-0 Inter Turku (Finland); Sheriff Tiraspol win 2-0 on aggregate.
UE Sant Julia (Andorra) 0-5 Levski Sofia (Bulgaria); Levski Sofia win 9-0 on aggregate.
BATE Borisov (Belarus) 2-0 Makedonija Skopje (Macedonia); BATE Borisov win 4-0 on aggregate.
FK Baki (Azerbaijan) 4-2 Ekranas Panevezys (Lithuania); FK Baki win 6-4 on aggregate.