Brage had a chance to take the lead in the first half as Kristian Andersen's free kick went just outside.
The Borlängel team accounted for a good first half in terms of play, but never felt really dangerous.
Instead, it was Kalmar who took the lead in the 61st minute when Bragmål guard Peter Rosendal tipped a cross to Fidan Aliti who nodded the lead.
Then a little hope was raised, however, when Kalmar's Piotr Johansson received his second yellow card for masking at a throw-in. Johansson couldn't believe his eyes.
Instead, 2-0 came in the final minutes through Herman Hallberg and after that Brage woke up a lot. But it was too late.
Jonathan Morsay put 2-1 up and then took the ball on a Kalmar arm which gave penalty for Brage in extra time. The penalty went in the bar, but on the second return Christian Kouakou put the receipt.
The meeting ended 4-2 to Kalmar over two games.
Kalmar star Viktor Elm did not play the return meeting because of knee problems.