Spin-orbit coupling has proven indispensable in the realization of topological materials and, more recently, Ising pairing in two-dimensional superconductors. This pairing mechanism relies on inversion symmetry-breaking and sustains anomalously large in-plane polarizing magnetic fields whose upper limit is predicted to diverge at low temperatures. Here, we show that the recently discovered superconductor few-layer stanene, epitaxially strained gray tin (α-Sn), exhibits a distinct type of Ising pairing between carriers residing in bands with different orbital indices near the Γ-point. The bands are split as a result of spin-orbit locking without the participation of inversion symmetry-breaking. The in-plane upper critical field is strongly enhanced at ultralow temperature and reveals the predicted upturn.