Photoacoustic imaging offers optical contrast images of human tissue at acoustic resolution, making it valuable for diverse clinical applications. However, quantifying tissue composition via optical contrast remains challenging due to the unknown light fluence within the tissue. Here, we propose a method that leverages known chromophores (e.g., arterial blood) to improve the accuracy of quantitative photoacoustic imaging. By using the optical properties of a known chromophore as a fluence marker and integrating it into the optical inversion process, we can estimate the unknown fluence within the tissue. Experimentally, we demonstrate that this approach successfully recovers both the spectral shape and magnitude of the optical absorption coefficient of an unknown chromophore. Additionally, we show that the fluence marker method enhances conventional optical inversion techniques, specifically (i) a straightforward iterative approach and (ii) a gradient-based method. Our results indicate an improvement in accuracy of up to 24.4% when comparing optical absorption recovery with and without the fluence marker. Finally, we present the method's performance and illustrate its applications in carotid plaque quantification.