Hyperpolarization approaches in magnetic resonance overcome the sensitivity limitations imposed by thermal magnetization and play an important role in a very wide range of modern applications. One of the newer strategies, variants of what is generically called SABRE, uses parahydrogen to form hydrides on transition metal catalysts, followed by reversible exchange to polarize target molecules in solution, and has produced large signal enhancements (≈104) on hundreds of different molecules, cheaply and rapidly. Most commonly, the sample is kept in a constant field, matched to make the hydride scalar coupling comparable to the frequency difference between hydride protons and target protons (≈6.5 mT) or hydride protons and target heteronuclei (≈0.5 µT). Here we demonstrate a different strategy, applicable to a wide range of target molecules, that produces field-independent spin order in the target molecules that is efficiently converted to magnetization. The observed signal is even independent of field direction, hence significant polarization can be achieved in a sample on a lab bench with no field control at all. We show this signal arises from creation of two-spin order in the target molecules and discuss multiple ways this strategy should expand SABRE generality and efficiency. We also show that, in many cases, the standard assumption in low-field SABRE of a starting state with only singlet polarization leads to incorrect results.