Bayer Leverkusen cruised through with a 4-0 win over FC Copenhagen making it 7-2 on aggregate.
Son Heung-Mon got the first only two minutes in after a defensive mix-up, and a deflected free-kick from Hakan Calhanoglu made it 2-0 five minutes later.
It was all but over when Stefan Kiessling got the third from the penalty spot after half an hour, and he bagged a second in the 65th minute.
Malmo overturned a first-leg deficit to see off Salzburg and book their place in the group stages.
The Austrians led 2-1 from last week, but were run off the park in a 3-0 defeat in Sweden.
They struck early, with captain Markus Rosenberg scoring a seventh minute penalty before Magnus Eriksson lashed in a 19th minute volley to make it 2-0.
Rosenberg then made sure of progress with his second six minutes from time.