Robert Hrgota and Peter Prevc both won their groups with impressive leaps, while Robert Kranjec and Jurji Tepes also fared well to edge them to a narrow victory over the host nation.
Slovenia's total of 479.1 points was just 1.2 better than the Poles, with Germany in third on 474.4.
The competition was intriguingly poised, only for the late evening final round to be called off. Organisers attempted to address the floodlight issue, but were forced to abandon the competition and declare the first round results final after 35 minutes.
The individual competition takes place on Saturday, with a start time which should ensure no need for floodlights and a full event.