A novel semantics-empowered two-user uplink non-orthogonal multiple access (NOMA) framework is proposed for resource efficiency enhancement. More particularly, a secondary far user (F-user) employs the semantic communication (SemCom) while a primary near user (N-user) employs the conventional bit-based communication (BitCom). The fundamental performance limit, namely semantic-versus-bit (SvB) rate region, of the proposed semantics-empowered NOMA framework is characterized. The equivalent SvB rate region achieved by the conventional BitCom-based NOMA is provided as the baseline scheme. It unveils that, compared to BitCom, SemCom can significantly improve the F-user's performance when its permitted transmit power is strictly capped, but may perform worse when its permitted transmit power is high. Guided by this result, the proposed semantics-empowered NOMA framework is investigated over fading channels. An opportunistic SemCom and BitCom scheme is proposed, which enables the secondary F-user to participate in NOMA via the most suitable communication method at each fading state, thus striking a good tradeoff between its own achieved performance and the interference imposed to the primary N-user. Two scenarios are considered for employing the opportunistic scheme, namely on-off resource management and continuous resource management. For each scenario, the optimal communication policy over fading channels is derived for maximizing the ergodic semantic rate achieved at the secondary F-user, subject to the minimum ergodic bit rate constraint of the primary N-user. Numerical results show that the proposed opportunistic scheme in both scenarios can achieve higher communication performance for NOMA than the baseline schemes merely employing SemCom or BitCom.