There is mounting evidence to suggest that individuals with chronic pain adjusted poorly to and were impacted negatively by social distancing measures during the lockdown. However, there is limited data on the factors that might protect against the negative effects associated with social distancing measures, as most research has been conducted in the general population and in the initial stages of the lockdown. The aim of this study was to improve the understanding of the role that resilience, happiness, and social support, all factors that are thought to have a protective role, played in the psychological function (measured as anxiety, depression, and stress) to the social distancing measures during the late stages of the lockdown in a sample of adults with and without chronic pain living in Spain. A group of 434 adults responded to an online survey and provided information on sociodemographic issues, which included measures of pain, perceived health and quality of life, depression, anxiety, stress, resilience, happiness, and social support. The data showed that individuals with chronic pain (N = 200; 46%) reported statistically significant worst psychological function, that is to say, they reported higher levels of anxiety, depression, and stress (all ps < 0.001). Resilience, social support, and happiness proved to be significant predictors of anxiety, depression, and stress, after controlling for the effects of age, gender, and chronic pain. Although the effect sizes were small to medium, they are consistent with the findings of other studies. The findings from this study provide important additional new information regarding the associations between resilience, happiness, and social support and the adjustment to the social distancing measures during the late stages of the lockdown. These findings can be used to develop programs to improve adjustment to and coping with the demands of social distancing measures.