This paper presents a spatio-temporal filtering approach for beamforming with phased arrays. The approach takes advantage of fast beam switching in modern Si-integrated phased arrays enabled by integrated digital circuits. The key technique involves fast switching among spatial beams created using the phased array. The resulting time-averaged beam represents a new spatial filter that might not have been feasible using the phase and gain control resolution available in the phased array. We present the underlying theory, and perform extensive system measurements on a software defined phased array radio based on state-of-the-art 28GHz phased array ICs. We demonstrate three use cases of spatio-temporal beam control in measurement: a) side lobe reduction, b) multi-armed beam formation and c) null pointing. We demonstrate how this approach can enable high precision beam control even in systems with limited phase shifter resolution and/or systems without any gain control per antenna element.