We present the results from the application of a two-dimensional emission line detection method, EMission-line two-Dimensional (EM2D), to the near-infrared G102 grism observations obtained with the Wide-Field Camera 3 (WFC3) as part of the Cycle 22 Hubble Space Telescope Treasury Program: the Faint Infrared Grism Survey (FIGS). Using the EM2D method, we have assembled a catalog of emission line galaxies (ELGs) with resolved star formation from each of the four FIGS fields. Not only can one better assess the global properties of ELGs, but the EM2D method allows for the analysis and improved study of the individual emission-line region within each galaxy. This paper includes a description of the methodology, advantages, and the first results of the EM2D method applied to ELGs in FIGS. The advantage of 2D emission line measurements includes significant improvement of galaxy redshift measurements, approaching the level of accuracy seen in high-spectral-resolution data, but with greater efficiency; and the ability to identify and measure the properties of multiple sites of star formation and over scales of ∼1 kpc within individual galaxies out to z ∼ 4. The EM2D method also significantly improves the reliability of high-redshift (z ∼ 7) Lyα detections. Coupled with the wide field of view and high efficiency of space-based grism observations, EM2D provides a noteworthy improvement on the physical parameters that can be extracted from grism observations.