Traditional data stream classification techniques assume that the stream of data is generated from a single non-stationary process. On the contrary, a recently introduced problem setting, referred to as Multistream Classification involves two independent non-stationary data generating processes. One of them is the source stream that continuously generates labeled data instances. The other one is the target stream that generates unlabeled test data instances from the same domain. The distributions represented by the source stream data is biased compared to that of the target stream. Moreover, these streams may have asynchronous concept drifts between them. The multistream classification problem is to predict the class labels of target stream instances, while utilizing labeled data available from the source stream. In this paper, we propose an efficient solution for multistream classification by fusing drift detection into online data shift adaptation. Experiment results on benchmark data sets indicate significantly improved performance over the only existing approach for multistream classification.