This paper presents a new mechanical joining process to assemble aluminum busbars in energy distribution systems. The process is based on the extension of injection lap riveting to the connection of busbars made from the same material as the rivets and requires redesigning the joints to ensure complete filling with good mechanical interlocking and appropriate contact pressures on the overlapping area. The experimental work was carried out in unit cells and involved the fabrication of the riveted joints and the evaluation of their electrical resistance at different service temperatures. Comparisons with the bolted joints that were fabricated and tested for reference purposes show that injection riveted joints provide lower values of electrical resistance and require much less space for assembly due to the absence of material protrusions above and below their surfaces. Numerical simulation with finite elements allows the relating of the reduction in electrical resistance with the changes in the electric current flow when the bolts are replaced by the new type of rivets. The experimental and numerical predictions revealed that the new type of rivets experience an increase in electrical resistance of up to 6 μΩ (30%) when the service temperature approaches 105 °C. Still, the resistance at this temperature (26.2 μΩ) is more than 3 times smaller than that of the bolted joints (80.5 μΩ).