Sr2IrO4 is a magnetic insulator assisted by strong spin-orbit coupling (SOC) whereas the Sr2RuO4 is a p-wave superconductor. The contrasting ground states have been shown to result from the critical role of the strong SOC in the iridate. Our investigation of structural, transport, and magnetic properties reveals that substituting 4d Ru4+ (4d4) ions for 5d Ir4+(5d5) ions in Sr2IrO4 directly adds holes to the t2g bands, reduces the SOC and thus rebalances the competing energies in single-crystal Sr2Ir1-xRuxO4. A profound effect of Ru doping driving a rich phase diagram is a structural phase transition from a distorted I41/acd to a more ideal I4/mmm tetragonal structure near x=0.50 that accompanies a phase transition from an antiferromagnetic-insulating state to a paramagnetic-metal state. We also make a comparison drawn with Rh doped Sr2IrO4, highlighting important similarities and differences.