A tangential entry premixing fuel injector ( 10 ) for a gas turbine engine combustor includes a pair of offset scrolls ( 18 ) whose ends define a pair of entry slots ( 36 ) for admitting primary combustion air tangentially into a mixing chamber ( 28 ) bounded by the scrolls ( 18 ) and by longitudinally spaced endplates ( 14, 16 ). An array of fuel injection passages ( 42 ) extends along the length of the slots. The passage array is configured to inject a primary fuel nonuniformly along the length of the air entry slots and to control the fuel penetration depth d in proportion to slot height H . The injector also includes a flame disgorging centerbody ( 48 ) having a bluff tip ( 54 ) longitudinally aligned with the injector's discharge plane ( 22 ) and a secondary fuel conduit ( 80 ) extending through the centerbody for discharging a secondary combustible fluid, preferably gaseous fuel, through a series of fuel discharge openings ( 84 ) in the tip ( 54 ). The flame disgorging centerbody improves fuel injector durability by resisting ingestion of combustion flame into the mixing chamber ( 28 ) and reliably disgorging any flame that is ingested. The controlled fuel penetration depth reinforces the flame disgorging capability of the centerbody by preventing fuel from penetrating into the slowly moving boundary layer attached to the centerbody ( 48 ). The bluff character of the centerbody, in combination with its longitudinal alignment with the fuel injector discharge plane, makes the centerbody capable of anchoring the flame at the discharge plane so that combustion occurs aft of the discharge plane where the combustion flame is unlikely to damage the scrolls or centerbody. Introduction of fuel or fuel and air through the openings in the bluff tip encourage the flame to become anchored to the tip and therefore spatially stabilizes the flame, resulting in additional attenuation of acoustic oscillations and further improved combustor durability. The longitudinally nonuniform injection of primary fuel compensates for any mixing nonuniformities attributable to the flame disgorging centerbody and therefore augments flame stability. The injector and an associated method of premixing fuel and air prior to combustion suppress formation of nitrous oxides, and improve the durability of both the injector and the combustor.