A novel \(H_{\textrm{c2}}\) suppression mechanism is theoretically proposed in a spin-triplet superconductor (SC) with equal spin pairs. We show that the upper critical field \(H_{\textrm{c2}}\) can be reduced from the orbital depairing limit \(H^{\textrm{orb}}_{\textrm{c2}}\) to arbitrarily small value, keeping the second-order phase transition nature. This mechanism is sharply different from the known Pauli–Clogston limit for a spin-singlet SC where the reduction is limited to \(\sim\) 0.3 \(H^{\textrm{orb}}_{\textrm{c2}}\) with the first-order transition when the Maki parameter goes infinity. This novel \(H_{\textrm{c2}}\) suppression mechanism is applied to \(\hbox {UTe}_2\) , which is a prime candidate for a spin-triplet SC, to successfully analyze the \(H_{\textrm{c2}}\) data for various crystalline orientations both under ambient and applied pressure, and to identify the pairing symmetry. It is concluded that the non-unitary spin-triplet state with equal spin pairs is realized in \(\hbox {UTe}_2\) , namely \(({\hat{b}}+i{\hat{c}})k_a\) in \(^3\hbox {B}_{\textrm{3u}}\) which is classified under finite spin–orbit coupling scheme.