We demonstrate an optical accelerator for convolutional neural networks using photonic tensor cores that achieves both state-of-the-art accuracy competitive with ideal floating point models, and unprecedented acceleration performance exceeding electronics by orders of magnitude. Across convolutional architectures and image datasets, the photonics-based hardware processes advanced inference workloads faster than alternate ASICs or GPUs. Additionally, power consumption and latency metrics are consistently lowered by using integrated optics -enabling real-time throughput while maintaining accuracy. By unlocking massively parallel and high bandwidth optical matrix operations, this approach promises to revolutionize compute-intensive CNN applications spanning medical imaging, scientific computing, autonomous systems and beyond. Fully integrated optical neural network accelerators now bring extraordinary speed, efficiency and scalability, opening new frontiers in artificial intelligence.