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This paper explores estimation of stress-strength reliability based on upper record values. When the strength and stress variables follow unit-Burr Ⅲ distributions, a generalized inferential approach is proposed for estimating stress-strength reliability (SSR). Under the common strength and stress parameter case, two types of pivotal quantities are constructed respectively, and then the generalized point and interval estimates for SSR are proposed in consequence, where the associated Monte-Carlo sampling approach is provided for computation. In addition, when strength and stress variables feature unequal model parameters, different generalized point and confidence interval estimates are also established in this regard. Extensive simulation studies are conducted to examine the behavior of proposed methods. Finally, a real-life data example is presented for illustration.