The RNA exosome fulfills important functions in the processing and degradation of numerous RNAs species. However, the mechanisms of recruitment to its various nuclear substrates are poorly understood. Using Epstein-Barr virus mRNAs as a model, we have discovered a novel function for the splicing factor SRSF3 in the quality control of nuclear mRNAs. We have found that viral mRNAs generated from intronless genes are particularly unstable due to their degradation by the nuclear RNA exosome. This effect is counteracted by the viral RNA-binding protein EB2 which stabilizes these mRNAs in the nucleus and stimulates both their export to the cytoplasm and their translation. In the absence of EB2, SRSF3 participates in the destabilization of these viral RNAs by interacting with both the RNA exosome and its adaptor complex NEXT. Taken together, our results provide direct evidence for a connection between the splicing machinery and mRNA decay mediated by the RNA exosome. Our results suggest that SRSF3 aids the nuclear RNA exosome and the NEXT complex in the recognition and degradation of certain mRNAs.