Following the outbreak of the COVID-19 pandemic, one of the first measures implemented in Italy was the transition from frontal teaching to online teaching. The sudden need to use technologies to perform their job has added a source of stress to teachers’ work: so-called technostress. The difficulties experienced in this transition may also have affected the perception of work-related well-being, although other variables, such as the perception of the meaningfulness of work, could alleviate this sense of uneasiness. The study aims to examine the relationships between technostress, online teaching, pleasure in working, and meaningful work perceptions among 219 teachers from different school grades through a moderated mediation model. The results confirm negative associations between technostress and pleasure in working, although this relationship varies according to the levels of perceived meaningfulness. Analyzing the factors related to teachers’ perceptions of their work, both in general and during the pandemic situation, is useful for tracing new coping strategies and planning interventions to implement new teaching methods. Further implications concerning the protective role of meaningful work are discussed.