This study applied the unified theory of acceptance and use of technology (UTAUT) model to examine the structural relations among performance expectancy, effort expectancy, social influence, facilitating conditions, behavioral intention, and actual use of generative AI in education among K-12 teachers. It also investigated the moderating roles of gender, age, professional development experience, and daily use experience. Survey data were collected from 347 K-12 teachers in South Korea. Structural equation modeling was employed to test the hypothesized relations, and multi-group analyses were conducted to examine group differences in associations across teacher subgroups. The results revealed that performance expectancy (β = .76, p < .001) was the factor most strongly associated with teachers’ behavioral intention to use generative AI in education. Social influence and facilitating conditions also showed significant positive associations in the overall model, whereas effort expectancy did not. However, effort expectancy showed a meaningful association among teachers aged 40 and above, as well as those with limited professional development or limited daily use experience. Moreover, behavioral intention significantly predicted actual use both directly and indirectly, mediating the effects of performance expectancy and facilitating conditions. This study extends the UTAUT framework by empirically validating teacher acceptance of generative AI in the K-12 educational context. The findings provide theoretical insights into technology acceptance mechanisms and offer practical and policy implications for effectively integrating generative AI into classroom teaching.