Early in his career, Stifunin competed with Nina Ulanova, coached by Andrei Filippov. The duo placed fifth at the 1996 World Junior Championships in Brisbane, Australia. In the 1996–97 season, they won gold at the 1997 World Junior Championships in Seoul, South Korea. After the event, Filippov moved to Australia and Ulanova/Stifunin joined Alla Belyaeva. They skated together until 1999, placing as high as fifth at the senior Russian Championships.