Both p150 and p110 isoforms of ADAR1 convert adenosine to inosine in double-stranded RNA (dsRNA). ADAR1p150 suppresses the dsRNA-sensing mechanism that activates MDA5-MAVS-IFN signaling in the cytoplasm. In contrast, the biological function of the ADAR1p110 isoform, which is usually located in the nucleus, is largely unknown. Here, we show that stress-activated phosphorylation of ADAR1p110 by MKK6-p38-MSK MAP kinases promotes its binding to Exportin-5 and its export from the nucleus. After translocating to the cytoplasm, ADAR1p110 suppresses apoptosis in stressed cells by protecting many antiapoptotic gene transcripts that contain 3'-untranslated-region dsRNA structures primarily comprising inverted Alu repeats. ADAR1p110 competitively inhibits binding of Staufen1 to the 3'-untranslated-region dsRNAs and antagonizes Staufen1-mediated mRNA decay. Our study reveals a new stress-response mechanism in which human ADAR1p110 and Staufen1 regulate surveillance of a set of mRNAs required for survival of stressed cells.