We report the detection and analysis of a radio flare observed on 17 April 2014 from Sgr A* at $9$ GHz using the VLA in its A-array configuration. This is the first reported simultaneous radio observation of Sgr A* across $16$ frequency windows between $8$ and $10$ GHz. We cross correlate the lowest and highest spectral windows centered at $8.0$ and $9.9$ GHz, respectively, and find the $8.0$ GHz light curve lagging $18.37^{+2.17}_{-2.18}$ minutes behind the $9.9$ GHz light curve. This is the first time lag found in Sgr A*s light curve across a narrow radio frequency bandwidth. We separate the quiescent and flaring components of Sgr A* via flux offsets at each spectral window. The emission is consistent with an adiabatically-expanding synchrotron plasma, which we fit to the light curves to characterize the two components. The flaring emission has an equipartition magnetic field strength of $2.2$ Gauss, size of $14$ Schwarzschild radii, average speed of $12000$ km s$^{-1}$, and electron energy spectrum index ($N(E)propto E^{-p}$), $p = 0.18$. The peak flare flux at $10$ GHz is approximately $25$% of the quiescent emission. This flare is abnormal as the inferred magnetic field strength and size are typically about $10$ Gauss and few Schwarzschild radii. The properties of this flare are consistent with a transient warm spot in the accretion flow at a distance of $10$-$100$ Schwarzschild radii from Sgr A*. Our analysis allows for independent characterization of the variable and quiescent components, which is significant for studying temporal variations in these components.
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