We present the first demonstration of THz-driven bunch compression and timing stabilization of a few-fC relativistic electron beam with kinetic energy of 2.5 MeV using quasi-single-cycle strong field THz radiation in a shorted parallel-plate structure. Compression by nearly a factor of 3 produced a 39 fs rms bunch length and a reduction in timing jitter by more than a factor of 2, to 31 fs rms, offering a significant improvement to beam performance for applications like ultrafast electron diffraction. This THz-driven technique provides a critical step towards unprecedented timing resolution in ultrafast sciences and other accelerator applications using femtosecond-scale electron beams.