The radical changes deriving from the COVID-19 emergency have heavily upset some of the most familiar routines of daily work life. Abruptly, many workers have been forced to face the difficulties that come with switching to remote working. Basing on the theoretical framework proposed by the Job Demands-Resources model, the purpose of this paper was to explore the effect of work overload (workload and techno overload), on behavioral stress, meant as an outcome linked to the health impairment process. Furthermore, the aim of the study was to explore the mediating role of job crafting, considered as a second-order construct consisting of two dimensions (increasing structural resources and increasing challenging demands) in the abovementioned relation. Participants were 530 workers experiencing remote working or work-from-home during the first COVID-19 lockdown in Italy (March–May 2020). Hypotheses were explored by using three different latent variables, measured reflexively through indicators on a 5-point scale, extracted from validated questionnaires. Data analysis was performed through Structural Equation Modeling; to test the mediation, bootstrap validation was computed (n = 2,000). Results showed that the mediation of job crafting was partial. More specifically, the direct effect between work overload and behavioral stress was positive; moreover, the indirect, negative effect through the mediation of job crafting was also significant. Therefore, results showed that job crafting can play a crucial role as a protective factor supporting the activation and adjustment of suitable resources; these resources can be useful to deal with the negative effects of work overload, particularly under the condition of heavy remote working and use of technologies, on individual outcomes. Starting from the current global scenario of the pandemic that has not yet ceased its effects, the study suggested decisive theoretical and practical implications. Accordingly, findings extended the current trends in occupational health psychology research, with special reference to the mainstream topic “work and COVID-19” in the Italian context. Finally, results can give suggestions to companies engaged in managing change, recommending that they build a collaborative workplace at the individual and collective level to implement job crafting interventions and enrich the personal and organizational resources of workers, which is useful cope with the current demands.