Acoustic Sensor Networks (ASNs) have a wide range of applications in natural and urban environment monitoring, as well as indoor activity monitoring. In-network classification is critically important in ASNs because wireless transmission costs several orders of magnitude more energy than computation. The main challenges of in-network classification in ASNs include effective feature selection, intensive computation requirement and high noise levels. To address these challenges, we propose a sparse representation based feature-less, low computational cost, and noise resilient framework for in-network classification in ASNs. The key component of Sparse Approximation based Classification (SAC), ℓ1 minimization, is a convex optimization problem, and is known to be computationally expensive. Furthermore, SAC algorithms assumes that the test samples are a linear combination of a few training samples in the training sets. For acoustic applications, this results in a very large training dictionary, making the computation infeasible to be performed on resource constrained ASN platforms. Therefore, we propose several techniques to reduce the size of the problem, so as to fit SAC for in-network classification in ASNs. Our extensive evaluation using two real-life datasets (consisting of calls from 14 frog species and 20 cricket species respectively) shows that the proposed SAC framework outperforms conventional approaches such as Support Vector Machines (SVMs) and k-Nearest Neighbor (kNN) in terms of classification accuracy and robustness. Moreover, our SAC approach can deal with multi-label classification which is common in ASNs. Finally, we explore the system design spaces and demonstrate the real-time feasibility of the proposed framework by the implementation and evaluation of an acoustic classification application on an embedded ASN testbed.