In additive manufacturing, it is imperative to increase print speeds, use higher viscosity resins, and print with multiple different resins simultaneously. To this end, we introduce a new UV-based photopolymerization 3D printing process exploiting a continuous liquid interface—the deadzone—mechanically fed with resin at elevated pressures through microfluidic channels dynamically created and integral to the growing part. Through such mass transport control, injection continuous liquid interface production, or iCLIP, accelerates printing speeds 5 to 10-fold over current methods such as continuous liquid interface production (CLIP), can utilize resins an order of magnitude more viscous than can CLIP, and can readily pattern a single heterogeneous object with different resins in all Cartesian coordinates. We characterize the process parameters governing iCLIP and demonstrate use-cases for rapidly printing carbon nanotube-filled composites, multi-material features with length scales spanning several orders of magnitude, and lattices with tuneable moduli and energy absorption.