Distributed energy resources (DER) such as solar photovoltaic (PV) interfaces with the utility grid by high-efficiency power electronic converters. This equipment is sometimes underutilized in terms of its power capacity; thus, the remaining capacity can be used to provide support to the distribution system. In this sense, this work assesses the performance of the three-level T-type quasi-impedance source inverter (3L-T-type qZSI) injecting not only active power to the grid, but also providing support to it by injecting reactive power and acting as an active power filter (APF) simultaneously. The global control strategy of the grid-connected inverter is derived from the instantaneous <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$i_{d}$ </tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$i_{q}$ </tex-math></inline-formula> power theory. The combination of an improved deadbeat current controller and a level-shifted carrier-based pulse-width-modulation (PWM) technique, using both the upper shoot-through (UST) and the lower shoot-through (LST) alternating states, allows a successful tracking of the current references. Both the dc-link voltage control and the neutral-point balancing are properly achieved by taking the advantage of the shoot-through (ST) states and the redundant states simultaneously. These control actions are implemented by simple proportional-integral (PI) controllers. The simulation and experimental results demonstrate the above-mentioned functionalities and verify the stability and good dynamic response of the grid-connected 3L-T-type qZSI.