Using the power transformation method, we introduce a generalized version of the unit Gumbel type-2 distribution. The new lifetime distribution is called the power unit Gumbel type-2 distribution (PUGT2D). The new distribution’s statistical and reliability properties are given, and some estimation methods are proposed for estimating the model parameters. The usefulness and flexibility of the new distribution are illustrated with real datasets. Results based on log-likelihood, information statistics, and goodness-of-fit test results showed that the PUGT2D better fits the data than the other competing distributions. Moreover, a new regression model based on the new distribution is introduced and demonstrated to exhibit superior applicability through a numerical example.