A technique dynamically enforces a best exit selection for a controlled prefix based on policies and real-time performance statistics in a computer network. A Master Controller (e.g., an Optimized Edge Routing, OER, Master Controller) of an autonomous system (AS) in the network selects a best exit from the AS for the controlled prefix, and conveys the selection to a border router having the selected exit. In response, the border router performs a parent lookup to determine whether the controlled prefix is reachable via the best exit. If so, the border router influences routing in the AS for the controlled prefix through the best exit by, e.g., injecting routes or modifying metrics of existing routes. The Master Controller (or border router) then verifies that the routes for the controlled prefix traverse the selected best exit. Notably, if a route does not traverse the selected best exit, the border router may try to influence the route again or remove the influence.