An increasing number of firms are outsourcing customer support to external service providers. This creates a triadic setting in which an outsourcing provider serves end customers on behalf of its clients. While outsourcing presents an opportunity to serve customers, service providers differ in their motivation and ability to fulfill customer needs. Prior research suggests that firms with a strong customer focus have an intrinsic motivation to address customer needs. We suggest that in an outsourcing context, this intrinsic motivation does not suffice. Using a Motivation–Opportunity–Ability framework, we posit that the effect of a provider's customer focus will be moderated by a set of relational, firm, and customer characteristics that affect its ability to serve end customers. We test our conceptualization among 171 outsourcing clients from the Netherlands and then validate these results among 135 Indian outsourcing providers. The findings reveal that customer‐focused providers achieve higher levels of customer need fulfillment but this effect is contingent on their ability to serve end customers. In particular, customer‐focused providers more effectively fulfill customer needs when clients and providers share close relational ties, when clients also have a high level of customer focus, and when end customer needs exhibit a low degree of turbulence. In addition, we find that, in turbulent markets, equipment‐related services offer greater opportunity for effective customer need fulfillment than other outsourced services.