Prediction of the effects of coronal mass ejections (CMEs) on Earth strongly depends on knowledge of the interplanetary magnetic field southward component, B z . Predicting the strength and duration of B z inside a CME with sufficient accuracy is currently impossible, forming the so-called B z problem. Here, we provide a proof-of-concept of a new method for predicting the CME arrival time, speed, B z , and resulting disturbance storm time (Dst) index on Earth based only on magnetic field data, measured in situ in the inner heliosphere (<1 au). On 2012 June 12–16, three approximately Earthward-directed and interacting CMEs were observed by the Solar Terrestrial Relations Observatory imagers and Venus Express (VEX) in situ at 0.72 au, 6° away from the Sun–Earth line. The CME kinematics are calculated using the drag-based and WSA–Enlil models, constrained by the arrival time at VEX, resulting in the CME arrival time and speed on Earth. The CME magnetic field strength is scaled with a power law from VEX to Wind. Our investigation shows promising results for the Dst forecast (predicted: −96 and −114 nT (from 2 Dst models); observed: −71 nT), for the arrival speed (predicted: 531 ± 23 km s−1; observed: 488 ± 30 km s−1), and for the timing (6 ± 1 hr after the actual arrival time). The prediction lead time is 21 hr. The method may be applied to vector magnetic field data from a spacecraft at an artificial Lagrange point between the Sun and Earth or to data taken by any spacecraft temporarily crossing the Sun–Earth line.