Many people struggling with mental health issues are unable to access adequate care due to high costs and a shortage of mental health professionals, leading to a global mental health crisis. Online mental health communities can help mitigate this crisis by offering a scalable, easily accessible alternative to in-person sessions with therapists or support groups. However, people seeking emotional or psychological support online may be especially vulnerable to the kinds of antisocial behavior that sometimes occur in online discussions. Moderation can improve online discourse quality, but we lack an understanding of its effects on online mental health conversations. In this work, we leveraged a natural experiment, occurring across 200,000 messages from 7,000 online mental health conversations, to evaluate the effects of moderation on online mental health discussions. We found that participation in group mental health discussions led to improvements in psychological perspective, and that these improvements were larger in moderated conversations. The presence of a moderator increased user engagement, encouraged users to discuss negative emotions more candidly, and dramatically reduced bad behavior among chat participants. Moderation also encouraged stronger linguistic coordination, which is indicative of trust building. In addition, moderators who remained active in conversations were especially successful in keeping conversations on topic. Our findings suggest that moderation can serve as a valuable tool to improve the efficacy and safety of online mental health conversations. Based on these findings, we discuss implications and trade-offs involved in designing effective online spaces for mental health support.