Udinese, like Malaga hit by a flurry of summer departures, held Braga 1-1 away and Belarus champions BATE Borisov appear on the brink of a second successive group stage appearance after a 2-0 home win over Israel's Hapoel Kiryat Shmona.
AEL Limassol, hoping to provide more success for Cyprus after APOEL's run to the quarter-finals last season, won 2-1 against Anderlecht who, like Tottenham Hotspur, are suffering the consequences of Chelsea winning the trophy last season.
Tottenham missed out altogether because Chelsea, who finished outside the top four in the English Premier League, took their place under UEFA's complex qualification system. Anderlecht, who should have gone straight into the group stage, were pushed back into the third qualification round.
Former Argentina defender Martin Demichelis put Malaga in front against group stage regulars Panathinaikos when he reacted quickly to flick home from close range in the 17th minute.
Portuguese Eliseu volleyed the second just after the half hour. Although Malaga did not concede, they may have been disappointed not to have added to their tally after they dominated the match.
Udinese, beaten at the same stage by Arsenal last season, went ahead in the 23rd minute against the run of play with a Dusan Basta header before Braga's Brazilian leftback Ismaily rifled in a stunning equaliser from long range in the 68th minute.
Defeat for Udinese against the Portuguese side would leave Italy with only two teams in the group stage after Serie A dropped below the Bundesliga in UEFA's coefficients system.
Anderlecht, who beat Lithuania's Ekranas 11-0 on aggregate in the previous round, found AEL a different proposition and they fell behind to a Dosa Junior goal in the 34th minute.
Dieudonne Mbokani levelled just after the hour for the Belgian champions only for Rui Miguel to put the Cypriots back in front 10 minutes later.
Anderlecht had Milan Jovanovic sent off for dissent on the touchline in the 75th minute, one minute after he had been substituted.
Vitali Rodionov scored both goals as BATE, full name Borisov Works of Automobile and Tractor Electric Equipment, ploughed on against Kiryat Shmona.
Milan Badelj scored in the 74th minute to give Croatian champions Dinamo Zagreb a 2-1 win at home to Maribor, from neighbouring Slovenia, in the night's other tie.
Badelj was playing his last game for Dinamo before a move to Hamburg SV, who are not involved in European competition this season.