Former UEFA Cup winners Feyenoord and Galatasaray bowed out of the competition as Rapid Bucharest and Tromso secured surprise places in the group stage.
Managerless Parma, who won the UEFA Cup twice in the 1990s but are now struggling to cope with financial hardship, face the prospect of elimination from the competition on Thursday.
Lazio face an ignominious exit from the UEFA Cup on Thursday if they fail to win their final group game away against Greek side Egaleo.
Resurgent Aston Villa pose a threat to Arsenal's title ambitions on Sunday afternoon.
Former UEFA Cup holders Feyenoord face an uphill task to stay in this season's competition after the 2002 winners suffered a 2-0 home defeat by Czech side Teplice in the first leg of the second round on Thursday.
Former European champions Barcelona and Liverpool turned on the style in the UEFA Cup on Wednesday to ease into the second round with big wins over East European opposition.
Inter Milan, Monaco, Juventus and Real Sociedad maintained their perfect starts in the Champions League on Tuesday while Celtic and Deportivo La Coruna picked up their first victories.
England striker Michael Owen became Liverpool's leading goalscorer of all time in Europe after netting in a 1-1 draw against Slovenia's Olimpija Ljubljana in the UEFA Cup on Wednesday.