Analysis of cellular pathways requires concentration measurements of dynamically interacting molecules within the 3D space of single living cells. Förster Resonance Energy Transfer (FRET) microscopy from widefield, confocal, and potentially from super-resolution microscopes can access this information; however, these measurements are distorted by the inherent 3D-blurring of optical imaging, spectral overlap of fluorophores and detection noise. We propose a mathematical model of these processes and demonstrate, through simulation, how these distortions limit the dynamic range and sensitivity of conventional FRET microscopy. Using this model, we devise and validate a new approach (called 3D-FRET Stoichiometry Reconstruction, 3DFSR) for reconstructing 3D distributions of bound and free fluorescent molecules. Previous attempts to reconstruct 3D-FRET data relied on sequential spectral unmixing and deconvolution, a process that corrupts the detection statistics. We demonstrate that 3DFSR is superior to these approaches since it simultaneously models spectral mixing, optical blurring and the detection noise. To achieve the full potential of this technique, we developed an instrument capable of acquiring 3D-FRET data rapidly and sensitively from single living cells. Compared with conventional FRET microscopy, our 3D-FRET reconstruction technique and new instrumentation provides orders of magnitude gains in both sensitivity and accuracy wherein sustained high resolution four-dimensional (4D; x,y,z,t) imaging of molecular interactions inside living cells was achieved. These results verify previous observations that Cdc42 signaling is localized to the advancing margins of forming phagosomes in macrophages.