An inseparable challenge associated with every random access network is the design of an efficient Collision Resolution Algorithm (CRA), since collisions cannot be completely avoided in such network. To maximize the collision resolution efficiency of a popular CRA, namely Binary Exponential Backoff (BEB), we propose a reactive backoff algorithm. The proposed backoff algorithm is reactive in the sense that it updates the contention window based on the previously selected backoff value in the failed contention stage to avoid a typical type of collision, referred as cross-collision. Cross-collision would occur if the contention slot pointed by the currently selected backoff value appeared to be present in the overlapped portion of the adjacent (the previous and the current) windows. The proposed reactive algorithm contributes to significant performance improvements in the network since it offers a supplementary feature of Cross Collision Exclusion (XCE) and also retains the legacy collision mitigation features. We formulate a Markovian model to emulate the characteristics of the proposed algorithm. Based on the solution of the model, we then estimate the throughput and delay performances of WLAN following the signaling mechanisms of the Distributed Coordination Function (DCF) considering IEEE 802.11b system parameters. We validate the accuracy of the analytical performance estimation framework by comparing the analytically obtained results with the results that we obtain from the simulation experiments performed in ns-2. Through the rigorous analysis, based on the validated model, we show that the proposed reactive cross collision exclusionary backoff algorithm significantly enhances the throughput and reduces the average packet delay in the network.