The　geometric　phase　is　of　fundamental　interest　and　plays　an　important　role　in　quantum　information　processing.　However,　the　definition　and　calculation　of　this　phase　for　open　systems　remain　problematic　due　to　the　lack　of　agreement　on　generalizations　of　the　parallel　transport　condition　to　mixed-state　nonunity　evolutions.　Here　we　tackle　this　problem　by　associating　the　open-system　geometric　phase　with　the　parallel　transport　of　the　joint　system-reservoir　state　and　find　that　the　associated　geometric　phase　can　be　calculated　when　the　total　Hamiltonian　is　time　independent.　Our　approach　not　only　provides　a　way　around　the　nonunitary　evolution　obstacle,　but　also　sheds　light　on　the　relation　between　the　geometric　phase　and　the　system-reservoir　entanglement.　Based　on　this　approach,　we　calculate　the　geometric　phase　of　different　quantum　systems　subject　to　energy　decay,　showing　that　it　is　robust　against　decoherence,　which　is　in　distinct　contrast　with　previous　results.