Ajax booked their place in the Champions League group stage with a comfortable 2-0 victory over Apoel Nicosia in Amsterdam.
After a goalless draw in Cyprus last week, last season's Champions League semi-finalists progressed thanks to goals from Edson Alvarez and Dusan Tadic.
Second-leg home advantage also proved important for Club Brugge and Slavia Prague as they followed Ajax through.
Brugge, 1-0 up from the first leg, beat Linz 2-1 after Hans Vanaken and Emmanuel Bonaventure scored either side of Klauss' penalty for the visitors.
And Slavia Prague accounted for Cluj, conquerors of Celtic in the previous qualifying round, thanks to Jan Boril's 66th-minute winner as they repeated a 1-0 first-leg success.
The group-stage draw takes place in Monaco on Thursday evening, when Premier League clubs Manchester City, Tottenham, Chelsea and Liverpool will also learn who their continental opponents are.
