Event detecting Wireless Sensor Networks (WSNs) with overlapping sensor nodes generate many redundant packets. Resource constraints in WSNs require minimizing the number of packets transmitted, so we want to eliminate all redundant packets. But this must be done carefully if we need to ensure reliable detection of all events happening across the network. Ensuring reliable transport of data is an important concern in resource-constrained WSNs. In a densely deployed sensor network, the sensing region of the sensor nodes often overlap with one another. Thus, data from sensor nodes that are in close proximity tend to be highly correlated. This introduces the concept of event reliability, where a reliable transfer of event data from each sensing region in a sensor network is sufficient. This paper proposes a distributed approach, i.e. Enhanced Event Reliability Protocol (EERP), that enables reliable transmission of event information to the sink node while minimizing redundant packets from nodes in close vicinity of one another. EERP builds on the spatio-temporal information of the originating nodes and employs an efficient combination of a greedy strategy with the use of multilateration algorithm in a unique way to perform event identification before reliably transmitting the event information towards the sink node. The performance of EERP is evaluated and compared against a base model, ERP and a commonly used scheme (SWIA). Our results show that EERP significantly improves event information delivery and energy efficiency while maintaining good coverage of events throughout the network.