Exciton-polaritons are quasiparticles with mixed photon and exciton character that demonstrate rich quantum phenomena, novel optoelectronic devices and the potential to modify chemical properties of materials. Organic materials are of current interest as active materials for their ability to sustain exciton-polaritons even at room temperature. However, within organic optoelectronic devices, it is often the 'dark' spin-1 triplet excitons that dominate operation. These triplets have been largely ignored in treatments of polaritons, which instead only consider the role of states that directly and strongly interact with light. Here we demonstrate that these 'dark' states can also play a major role in polariton dynamics, observing polariton population transferred directly from the triplet manifold via triplet-triplet annihilation. The process leads to polariton emission that is longer-lived (>μs) even than exciton emission in bare films. This enhancement is directly linked to spin-2 triplet-pair states, which are formed in films and microcavities by singlet fission or triplet-triplet annihilation. Such high-spin multiexciton states are generally non-emissive and cannot directly couple to light, yet the formation of polaritons creates for them entirely new radiative decay pathways. This is possible due to weak mixing between singlet and triplet-pair manifolds, which - in the strong coupling regime - enables direct interaction between the bright polariton states and those that are formally non-emissive. Our observations offer the enticing possibility of using polaritons to harvest or manipulate population from states that are formally dark.