This study concerns the problem of controlling multiclass (elastic, inelastic and unresponsive) Internet traffic without sacrificing quality of service (QoS) by adopting a unified 'resource allocation and traffic management' approach. The aim is to minimise the need for relying on dedicated QoS traffic control mechanisms in order to avoid spiralling complicatedness that, in practice, leads to 'robust yet fragile' Internet. In order to address this challenge, the authors first introduce an end-to-end non-convex network utility maximisation-based resource allocation algorithm to guarantee enhanced QoS to elastic and inelastic flows. Then, a pricing-based fair and scalable traffic management scheme, called Purge, is introduced to protect transmission control protocol-friendly traffic from unfairness attacks by unresponsive flows. Finally, the main contribution of this work, the unified algorithm, is developed by adapting Purge to complement link-control of the proposed resource allocation algorithm to enable it to enforce fairness while maintaining a scalable network core. The unified approach thus delivers QoS guarantees for multiclass traffic.