Kristianstad put in a higher gear in the second half and is now second in their group, on the same points as one Berlin with two more games played.
Adam Nyfjäll was the top scorer with seven goals scored while Fredrik Petersen and Teitur Örn Einarsson accounted for five pods each against Tatran Presov who is last in the table.
The next match for the Scanians is already waiting in two days, at home against Ystads IF in the league game.
For Alingsås, things went worse in Europe on Tuesday.
Away against Montpellier, who won the Champions League as late as 2018, they fell with a clear 21-32. Jonathan Sandberg scored six goals for Alingsås, which is in fourth place in the table of six teams.