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We present multiwavelength photometric and spectroscopic observations of SN 2019ein, a high-velocity Type Ia supernova (SN Ia) discovered in the nearby galaxy NGC 5353 with a two-day nondetection limit. SN 2019ein exhibited some of the highest measured expansion velocities of any SN Ia, with a Si II absorption minimum blueshifted by 24,000 km s$^{-1}$ at 14 days before peak brightness. More unusually, we observed the emission components of the P Cygni profiles to be blueshifted upward of 10,000 km s$^{-1}$ before B-band maximum light. This blueshift, among the highest in a sample of 28 other Type Ia supernovae, is greatest at our earliest spectroscopic epoch and subsequently decreases toward maximum light. We discuss possible progenitor systems and explosion mechanisms that could explain these extreme absorption and emission velocities. Radio observations beginning 14 days before B-band maximum light yield nondetections at the position of SN 2019ein, which rules out symbiotic progenitor systems, most models of fast optically thick accretion winds, and optically thin shells of mass $\lesssim 10^{-6}$ M$_\odot$ at radii $< 100$ AU. Comparing our spectra to models and observations of other high-velocity SNe Ia, we find that SN 2019ein is well fit by a delayed-detonation explosion. We propose that the high emission velocities may be the result of abundance enhancements due to ejecta mixing in an asymmetric explosion, or optical depth effects in the photosphere of the ejecta at early times. These findings may provide evidence for common explosion mechanisms and ejecta geometries among high-velocity SNe Ia.