This paper introduces Implicit-JSCC, a novel overfitted joint source-channel coding paradigm that directly optimizes channel symbols and a lightweight neural decoder for each source. This instance-specific strategy eliminates the need for training datasets or pre-trained models, enabling a storage-free, modality-agnostic solution. As a low-complexity alternative, Implicit-JSCC achieves efficient image transmission with around 1000x lower decoding complexity, using as few as 607 model parameters and 641 multiplications per pixel. This overfitted design inherently addresses source generalizability and achieves state-of-the-art results in the high SNR regimes, underscoring its promise for future communication systems, especially streaming scenarios where one-time offline encoding supports multiple online decoding.