Before kick-off, Kalmar's Erik Israelsson was thanked.
The 33-year-old, with 175 matches in the Allsvenskan, decided just over a month ago that his career is over.
On the field, it was Mjällby who took the lead in the first half through Jacob Bergström.
The striker, who has been out for much of the season with a head injury, headed in the lead after 21 minutes.
Kalmar owned the game and possession but failed to find their way in the offensive penalty area.
In the second half, many called for a penalty kick for the home team after Oliver Berg fell in the penalty area, but the referee acquitted.
Instead, it was Mjällby who extended his lead.
Viktor Gustafson struck with a real projectile that found its way into the crossbar.
The 2-0 goal took the air out of Kalmar, who failed to get up.
Even if they managed to reduce it at the end.
A heavy loss for Henrik Rydström's gang, who lose important points in the even fight for the European places.
The loss is Kalmar's first since August 14.