Network monitoring data generally consists of hundreds of counters periodically collected in the form of time-series, resulting in a complex-to-analyze multivariate time-series (MTS) process. Traditional time-series anomaly detection methods target univariate time-series analysis, which makes the MTS analysis cumbersome and prohibitively complex. We present DC-VAE (Dilated Convolutional -Variational Auto Encoder), a novel approach to anomaly detection in MTS data, leveraging convolutional neural networks (CNNs) and variational autoencoders (VAEs). DC-VAE detects anomalies in MTS data through a single model, exploiting temporal information without sacrificing computational and memory resources. In particular, instead of using recursive neural networks, large causal filters, or many layers, DC-VAE relies on Dilated Convolutions (DC) to capture long and short-term phenomena in the data. We evaluate DC-VAE on the detection of anomalies in the TELCO TELeCOmmunication-networks dataset, a large-scale, multi-dimensional network monitoring dataset collected at an operational mobile Internet Service Provider (ISP), where anomalous events were manually labeled by experts during seven months, at a five-minutes granularity. We benchmark DC-VAE against a broad set of traditional time-series anomaly detectors from the signal processing and machine learning domains. We also evaluate DC-VAE in open, publicly available datasets, comparing its performance against other multivariate anomaly detectors based on deep learning generative models. Results confirm the advantages of DC-VAE, both in terms of MTS data modeling, as well as for anomaly detection. For the sake of reproducibility and as an additional contribution, we make the TELCO dataset publicly available to the community and openly release the code implementing DC-VAE.