Handling of submicron-sized objects is important in many biochemical and biomedical applications, but few methods today can precisely manipulate this range of particles. We present gradient acoustic focusing that enables flow-through particle separation of submicron particles and cells and we apply it for separation of bacteria from blood lysate to facilitate their detection in whole blood for improved diagnostics. To control suspended objects below the classical 2µm size limit for acoustic focusing, we introduce a co-flowing acoustic impedance gradient to generate a stabilizing acoustic volume force that supresses acoustic streaming. The method is validated theoretically and experimentally using polystyrene particles, Staphylococcus aureus, Streptococcus pneumoniae and Escherichia coli. The applicability of the method is demonstrated by the separation of bacteria from selectively chemically lysed blood. Combined with downstream operations, this new approach opens up for novel methods for sepsis diagnostics.