For a binary protostellar outflow system in which its members are located close to each other (the separation being smaller than the addition of the widths of the flows) and with large opening angles, the collision seems unavoidable regardless of the orientation of the outflows. This is in contrast to the current observational evidence of just a few regions with indications of colliding outflows, which could also suggests that the average distance between protostars is larger than the width of the flows. Here, using sensitive observations of the Atacama Large Millimeter/Submillimeter Array, we report resolved images of carbon monoxide (CO) toward the binary flows associated with the BHR 71 protostellar system. These images reveal for the first time solid evidence that their flows are partially colliding, increasing the brightness of the CO, the dispersion of the velocities in the interaction zone, and changing part of the orientation in one of the flows. Additionally, this impact opened the possibility of knowing the three-dimensional geometry of the system, revealing that one of its components (IRS 2) should be closer to us.