After just under half an hour, Mjällby scored 1-0.
The unmarked Carlos Gracia appeared at the far post and headed in Otto Rosengren's left corner.
Before that, Jakob Bergström had a shot on the outside of the far left post for Mjällby.
At the beginning of the second half, Mjällby scored again with a headed goal.
On a free kick, Adam Sthål headed in 2-0 and sent Varberg towards the qualifiers.
The confusion was total in Varberg at the 3-0 goal.
A failed backward header gave Silas Nwankwo a clear path towards goal.
His first finish was saved by Varberg's returning veteran goalkeeper Stojan Lukic, 42, but courted by three players, Nwankwo tapped home the rebound.
Alexander Johansson's 3-1 reduction was too late.
It was really bad at 4-1 when Gideon Mensah pushed the ball into his own goal after getting the shot from Mjällby's Mamudo Moro completely wrong.