We demonstrate edge-emitting exciton-polariton (polariton) laser operation from 5 to 300 K and polariton amplifiers based on polariton modes within ZnO waveguides. The guided mode dispersion below and above the lasing threshold is directly measured using gratings placed on top of the sample, fully demonstrating the polaritonic nature of the lasing modes. The threshold is found to be smaller than that expected for radiative polaritons in planar ZnO microcavities below 150 K and comparable above. These results open up broad perspectives for guided polaritonics by enabling easier and more straightforward implementation of polariton integrated circuits that exploit fast propagating polaritons, and, possibly, topological protection.