Despite the numerous static and dynamic program analysis techniques in the literature, data races remain one of the most common bugs in modern concurrent software. Further, the techniques that do exist either have limited detection capability or are unsound, meaning that they report false positives. We present a sound race detection technique that achieves a provably higher detection capability than existing sound techniques. A key insight of our technique is the inclusion of abstracted control flow information into the execution model, which increases the space of the causal model permitted by classical happens-before or causally-precedes based detectors. By encoding the control flow and a minimal set of feasibility constraints as a group of first-order logic formulae, we formulate race detection as a constraint solving problem. Moreover, we formally prove that our formulation achieves the maximal possible detection capability for any sound dynamic race detector with respect to the same input trace under the sequential consistency memory model. We demonstrate via extensive experimentation that our technique detects more races than the other state-of-the-art sound race detection techniques, and that it is scalable to executions of real world concurrent applications with tens of millions of critical events. These experiments also revealed several previously unknown races in real systems (e.g., Eclipse) that have been confirmed or fixed by the developers. Our tool is also adopted by Eclipse developers.