In this paper, we propose a score-informed source separation framework based on non-negative matrix factorization (NMF) and dynamic time warping (DTW) that suits for both offline and online systems. The proposed framework is composed of three stages: training, alignment, and separation. In the training stage, the score is encoded as a sequence of individual occurrences and unique combinations of notes denoted as score units. Then, we proposed a NMF-based signal model where the basis functions for each score unit are represented as a weighted combination of spectral patterns for each note and instrument in the score obtained from a trained a priori over-completed dictionary. In the alignment stage, the time-varying gains are estimated at frame level by computing the projection of each score unit basis function over the captured audio signal. Then, under the assumption that only a score unit is active at a time, we propose an online DTW scheme to synchronize the score information with the performance. Finally, in the separation stage, the obtained gains are refined using local low-rank NMF and the separated sources are obtained using a soft-filter strategy. The framework has been evaluated and compared with other state-of-the-art methods for single channel source separation of small ensembles and large orchestra ensembles obtaining reliable results in terms of SDR and SIR. Finally, our method has been evaluated in the specific task of acoustic minus one, and some demos are presented.