Chemical abundances are presented for 25 M31 globular clusters (GCs), based on moderately high resolution (R = 22,500) H-band integrated light (IL) spectra from the Apache Point Observatory Galactic Evolution Experiment (APOGEE). Infrared (IR) spectra offer lines from new elements, lines of different strengths, and lines at higher excitation potentials compared to the optical. Integrated abundances of C, N, and O are derived from CO, CN, and OH molecular features, while Fe, Na, Mg, Al, Si, K, Ca, and Ti abundances are derived from atomic features. These abundances are compared to previous results from the optical, demonstrating the validity and value of IR IL analyses. The CNO abundances are consistent with typical tip of the red giant branch stellar abundances but are systematically offset from optical Lick index abundances. With a few exceptions, the other abundances agree between the optical and the IR within the 1σ uncertainties. The first integrated K abundances are also presented and demonstrate that K tracks the α elements. The combination of IR and optical abundances allows better determinations of GC properties and enables probes of the multiple populations in extragalactic GCs. In particular, the integrated effects of the Na/O anticorrelation can be directly examined for the first time.