A goal in each half from local boys Ale Fuentes (photo) and Adrian Machín was enough to claim all three points.
Fuentes gave the Rojillos a 0-1 half time lead with a strike on the half hour. Machín came off the bench to extend his sides lead to 0-2 in the 64th minute.
The home side made it a nervous ending with an 88th minute goal pulling the score back to 1-2.
Lanzarote deservedly claim all three points and are now level with UD Las Palmas B following their draw yesterday.
The Rojillos are one point behind league leaders CD Tenerife B but they can extend that lead with a win in Fuerteventura against UD Gran Tarajal.
Also if U.S.Yaiza win later today by two clear goals they will leapfrog Lanzarote into third spot.
Next Sunday 4th February Lanzarote are at home versus UD Gran Tarajal at 12 noon.
0-1 min 30 Ale Fuentes
0-2 min 64 Adrian Machín
1-2 min 88 Eleder Marrero