Having avoided relegation every year since 2001, Israel will begin its 2018 campaign away to South Africa in February.
With Romania dropping their most senior players, Israel started as strong favourites but had to sweat in the first match as Edan Leshem (285) took five sets and three and a half hours to overcome Dragos Dima (463).
Dudi Sela (65) then had a straightforward three-set victory over Nicolae Frunza (600) before teaming up with Jonathan Erlich to clinch the contest with a straight sets win over Vasile Antonescu and Bogdan Borza.
On the final day, Mor Bulis (590) earned his first-ever Davis Cup victory, beating Antonescu (685) and Leshem completed the rout by beating Frunza.