Victor Rodriguez's header after five minutes settled this six-pointer at the Martinez Valero.
The hosts, who sat 18th in the table prior to kickoff, behind Almeria on goal difference, climb to 14th following the win.
Fran Escriba could not have wished for a better start as he watched his side take the lead after just five minutes.
Top goalscorer Jonathas stood up a fine cross after an exquisite bit of skill as Victor nodded home from six yards.
The visitors had to wait some 38 minutes before threatening parity, but Sebastian Dubarbier saw his sweetly-struck free kick bounce off the post.
Both sides spurned golden opportunities to score before the break as Jonathas latched onto Victor's defence-splitting pass, but his effort was parried by Julian, while Miguel Angel Corona saw his shot expertly tipped over by Przemyslaw Tyton.
It could have been 2-0 on 51 minutes as Victor missed the chance to secure his brace by side-footing Faycal Fajr's inch-perfect cross wide.
Chances were at a premium for both sides for much of the second half, but Garry Rodrigues should have wrapped up the points when Julian pushed his tame effort past the post.
Wellington Silva almost made Rodrigues pay, but Tyton pushed the Brazilian's fierce effort over the bar in the latter stages as Elche held on.