In　light　of　the　drastically-increasing　demands　on　ubiquitous　information　acquisition　and　exchange,　battery-powered　devices　are　playing　a　more　critical　role　in　wireless　networking,　which　inspires　and　expedites　the　development　of　energy-harvesting　techniques.　The　sustainability　requirements　for　such　devices　include　two　mutual-impacting　dimensions:　energy　supply　avoiding　battery　outage　and　stable　transmissions　avoiding　buffer　overflow.　We　in　this　paper　propose　a　power-and-rate　adaption　scheme　subject　to　the　constraints　on　buffer-overflow　probability　and　battery-outage　probability　in　energy-harvesting　enabled　networks.　The　two　probability　constraints　address　the　statistical　assurance　for　the　two-dimensional　sustainability,　which　is　suitable　to　dealing　with　the　highly　unpredictable　energy-harvesting　and　channel　fading　statuses.　Specifically,　by　applying　the　asymptotic　queuing　analyses　to　data-transmission　and　energy-harvesting　processes,　we　can　characterize　both　of　the　battery-outage　and　buffer-overflow　probabilities　via　the　effective-capacity/-bandwidth　theories.　Then,　we　formulate　the　effective-capacity　optimization　problem,　which　maximizes　the　sustainable　throughput　while　complying　with　the　statistical　buffer-overflow　and　battery-outage　constraints,　and　solve　for　the　optimal　power-adaptation　scheme.　We　also　conducted　abundant　simulations　to　evaluate　our　scheme＇s　performances,　demonstrate　the　superiority　of　our　proposed　scheme　over　existing　baseline　schemes,　as　well　as　study　the　impact　of　sustainability　requirements　on　the　performances.　©　2015　IEEE.