Brain-inspired computer architecture facilitates low-power and low-latency deep neural network inference for edge AI applications. The hardware performance crucially hinges on the quantity of non-zero activations (referred to as events) during DNN inference. Thus, we propose a novel event suppression method, dubbed ELSE, which enhances DNN Efficiency via Line-based Sparsity Exploration. Specifically, it exploits spatial correlation between adjacent lines in activation maps to reduce network events. Our method achieves a reduction in event-triggered computation ranging from 2.43x to 5.75x for object detection and from 3.7x to 6.49x for pose estimation across various networks compared to conventional processing. Moreover, we empirically demonstrate that a layerwise mixed approach incorporating ELSE with other prominent event suppression methods enables a substantial enhancement in computation savings by up to 8.83x in spatial suppression, or effectively reduces memory consumption by 2~4x in temporal suppression. The results highlight ELSE's significant event suppression ability and its capacity to deliver complementary performance enhancements for state-of-the-art (SOTA) approaches.