The 2016 Vela glitch observed by the Mount Pleasant radio telescope provides the first opportunity to study pulse-to-pulse dynamics of a pulsar glitch, opening up new possibilities to study the neutron star’s interior. We fit models of the star’s rotation frequency to the pulsar data, and present the following three results. First, we constrain the glitch rise time to less than 12.6 s with 90% confidence, almost three-times shorter than the previous best constraint. Second, we find definitive evidence for a rotational-frequency overshoot and fast relaxation following the glitch. Third, we find evidence for a slowdown of the star’s rotation immediately before the glitch. The overshoot is predicted theoretically by some models; we discuss implications of the glitch rise and overshoot decay times on internal neutron-star physics. The slowdown preceding the glitch is unexpected; we propose the slowdown may trigger the glitch by causing a critical lag between crustal superfluid and the crust.