This paper introduces improved methods for sub-event detection in social media streams, by applying neural sequence models not only on the level of individual posts, but also directly on the stream level. Current approaches to identify sub-events within a given event, such as a goal during a soccer match, essentially do not exploit the sequential nature of social media streams. We address this shortcoming by framing the sub-event detection problem in social media streams as a sequence labeling task and adopt a neural sequence architecture that explicitly accounts for the chronological order of posts. Specifically, we (i) establish a neural baseline that outperforms a graph-based state-of-the-art method for binary sub-event detection (2.7% micro-F1 improvement), as well as (ii) demonstrate superiority of a recurrent neural network model on the posts sequence level for labeled sub-events (2.4% bin-level F1 improvement over non-sequential models).