Light propagating in tissue attains a spectrum that varies with location due to wavelength-dependent fluence attenuation, an effect that causes spectral corruption. Spectral corruption has limited the quantification accuracy of optical and optoacoustic spectroscopic methods, and impeded the goal of imaging blood oxygen saturation (sO2) deep in tissues; a critical goal for the assessment of oxygenation in physiological processes and disease. Here we describe light fluence in the spectral domain and introduce eigenspectra multispectral optoacoustic tomography (eMSOT) to account for wavelength-dependent light attenuation, and estimate blood sO2 within deep tissue. We validate eMSOT in simulations, phantoms and animal measurements and spatially resolve sO2 in muscle and tumours, validating our measurements with histology data. eMSOT shows substantial sO2 accuracy enhancement over previous optoacoustic methods, potentially serving as a valuable tool for imaging tissue pathophysiology.