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.
Levy said: "To remain in Group One is a major achievement from our point of view and we did the job in the best possible way. It all went very smoothly.
"Dudi and Jonathan bring enormous experience while we have talented youngsters coming through.
"Leshem's two victories will give him enormous confidence for the future."