Reproduction of high quality spatial sound has gained considerable importance with the recent technology developments in the fields of virtual and augmented reality. Recently, the reproduction of binaural signals in the Spherical-Harmonics (SH) domain has been proposed. This is performed by using SH representations of the sound-field and the Head-Related Transfer Function (HRTF). These processes offer the flexibility to control the reproduced binaural signals, by manipulating the sound-field or the HRTFs using algorithms that operate directly in the SH domain. However, in most practical cases, the binaural reproduction is order-limited, which introduces truncation error that has a detrimental effect on the perception of the reproduced signals, mainly due to the truncation of the HRTF. A recent study showed that pre-processing of the HRTF by ear-alignment reduces its effective SH order, which may be beneficial for alleviating the above effect. In this paper, a method to incorporate the pre-processed ear-aligned HRTF into the binaural reproduction process is presented. The method uses Ambisonics representation of the sound-field formulated at the two ears, and is denoted here as Bilateral Ambisonics. The proposed method leads to a significant reduction in errors due to the limited-order reproduction, which yields a substantial improvement in perceived binaural reproduction quality even with SH as low as first order.