An enhanced delayed fluorescence is demonstrated experimentally in tetracene single crystals strongly coupled to optical modes in open cavities formed by arrays of plasmonic nanoparticles. Hybridization of singlet excitons with collective plasmonic resonances in the arrays leads to the splitting of the material dispersion into a lower and an upper polariton band. This splitting significantly modifies the dynamics of the photoexcited tetracene crystal, resulting in an increase of the delayed fluorescence by a factor of 4. The enhanced delayed fluorescence is attributed to the emergence of an additional radiative decay channel, where the lower polariton band harvests long-lived triplet states. There is also an increase in total emission, which is wavelength dependent, and can be explained by the direct emission from the lower polariton band, the more efficient light out-coupling, and the enhancement of the excitation intensity. The observed enhanced fluorescence opens the possibility of efficient radiative triplet harvesting in open optical cavities, to improve the performance of organic light emitting diodes.