We report follow-up observations of the Class I binary protostellar system L1551 NE in the C18O (3--2) line with the SMA in its compact and subcompact configurations. Our previous observations at a higher angular resolution in the extended configuration revealed a circumbinary disk exhibiting Keplerian motion. The combined data having more extensive spatial coverage (~140 - 2000 AU) verify the presence of a Keplerian circumbinary disk, and reveals for the first time a distinct low-velocity (~< +-0.5 km s-1 from the systemic velocity) component that displays a velocity gradient along the minor axis of the circumbinary disk. Our simple model that reproduces the main features seen in the Position-Velocity diagrams comprises a circumbinary disk exhibiting Keplerian motion out to a radius of ~300 AU, beyond which the gas exhibits pure infall at a constant velocity of ~0.6 km s-1. The latter is significantly smaller than the expected free-fall velocity of ~2.2 km s-1 onto the L1551 NE protostellar mass of ~0.8 Msun at ~300 AU, suggesting that the infalling gas is decelerated as it moves into regions of high gas pressure in the circumbinary disk. The discontinuity in angular momenta between the outer infalling gas and inner Keplerian circumbinary disk implies an abrupt transition in the effectiveness at which magnetic braking is able to transfer angular momentum outwards, a result perhaps of the different plasma beta and ionization fractions between the outer and inner regions of the circumbinary disk.