This paper investigates the presence of a causal relationship between energy poverty and income poverty in the EU Member States through a Panel Vector Autoregressive specification, and controlled with a set of explanatory variables collected from the Eurostat energy database and the OECD environment database for 2007–2018. Deepening the nexus between energy poverty and income poverty is a relevant issue for tailoring policies to tackle poverty and improve the well-being of citizens, supporting the policy makers in the allocation of planned funds provided by the Recovery plan, “Next Generation EU”. The results of the panel VAR model estimation and Dumitrescu and Hurlin test suggest that there will be no change in the long-run equilibrium when income poverty remains constant. Moreover, the reduction in energy poverty is expected to have a positive effect in terms of overall economic poverty reduction. Finally, there is evidence that substituting fossil fuels with renewables helps to reduce energy poverty and widespread poverty due to the leverage effect on economic development as well as to support the achievement of some of the 17 Sustainable Development Goals addressed by United Nations.