Recently evidence has been reported for a low-level velocity oscillation with a period of 39 +/- 1 Mpc (127 +/- 3 Myr) superimposed on the Hubble flow. Like the Hubble flow, this oscillation is assumed to be an expansion and contraction of space itself. If space is oscillating as it expands and the Hubble flow contains a superimposed velocity ripple, matter on Earth will experience alternating accelerations and decelerations relative to the rest of the matter in the Universe. The acceleration curve can be obtained from the velocity oscillation curve simply by taking the magnitude of the derivative of the velocity curve and the acceleration curve is found here to have a period of 63.5+/-1.5 Myr. Evidence has also been claimed recently for an ubiquitous ~62 +/-3 Myr periodic fluctuation superimposed on general trends in the fossil biodiversity on Earth. The periods of the acceleration curve oscillation and fossil biodiversity fluctuations are thus identical within the errors. A second, weaker fluctuation is also detected in both the Hubble flow and fossil biodiversity trends. They too have identical periods of ~140 Myr. From this excellent agreement it is argued here that it is the oscillation in the Hubble flow, through an inertia-like phenomenon involving all the matter in the Universe that has produced the fluctuations in the fossil biodiversity on Earth. This may represent the first instance where observational evidence supporting Mach's Principle of Inertia has been found.