From:http://www.etymonline.com/s7etym.htm
Slav - 14c., Sclave, from M.L. Sclavus, from late Gk. Sklabos, from O.Slav. Sloveninu "Slav," probably related to slovo "word, speech," which suggests the name originally meant member of a speech community. Spelled Slave c.1788-1866, infl. by Fr. and Ger. Slave.
slave - c.1300, from O.Fr. esclave, from M.L. Sclavus "slave," originally "Slav," so called because of the many Slavs sold into slavery by conquering peoples. The verb meaning "work like a slave" is first recorded 1719. Slavery is from 1551; slavish "servilely imitative" is from 1753. O.E. Wealh "Briton" also began to be used in the sense of "serf, slave" c.850; and Skt. dasa-, which can mean "slave," is apparently connected to dasyu- "pre-Aryan inhabitant of India." More common O.E. words for slave were þeow (related to þeowian "to serve") and þræl (see thrall). The Slavic words for "slave" (Rus. rab, Serbo-Croatian rob, O.C.S. rabu) are from O.Slav. *orbu, from the PIE base *orbh- (also source of orphan) the ground sense of which seems to be "thing that changes allegiance" (in the case of the slave, from himself to his master). The Slavic word is also the source of robot.

I find it surprising that the terms used by the Greeks or Romans would have given way so completely to this relatively late word.