This phase I/II partially randomized trial studies the side effects and the best dose of ruxolitinib phosphate when given together with paclitaxel and carboplatin and to see how well they work in treating patients with stage III-IV epithelial ovarian, fallopian tube, or primary peritoneal cancer. Ruxolitinib phosphate may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as paclitaxel and carboplatin, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving ruxolitinib phosphate together with paclitaxel and carboplatin may be a better treatment for epithelial ovarian, fallopian tube, or primary peritoneal cancer.