Konstantinos Makridis opened the scoring for the hosts in the first quarter of an hour.
Two goals from Efstathios Aloneftis then sealed the win for the home side and ensured that a qualifying campaign that started with a 13-0 hammering by Germany continues to be an ordeal for the tiny landlocked republic.
Andy Selva blasted an early free-kick over for San Marino but at the other end, Federico Valentini did well to field a shot from Yiannis Okkas.
That was the prelude to the opener and it was Aloneftis who supplied it with a cross which Makridis headed home.
Makridis soon tried to double his tally with an ambitious effort from distance and Valentini did well to foil Stelios Okkarides. He then saved further efforts from Okkas and Michalis Konstantinou. Elias Charalamboulos also missed as the Cypriots dominated proceedings.
They made their dominance pay by scoring a second six minutes before the break. Aloneftis converted a free-kick from outside the area after a foul on Konstantinou by Fabio Vitaioli.
Aloneftis missed the chance to score again early in the second period but then Selva gave San Marino a rare lift with a shot from distance that was not far off the mark.
Manuel Marani missed with another long-range shot for the visitors and Selva spurned another half-chance but they were trying to stem a Cypriot tide.
Despite the best efforts of the visitors it was Cyprus who would score the third and final goal of the match.
Makridis played the role of provider as he teed up Aloneftis who completed the job with his left foot to secure three points for Cyprus and leave San Marino looking out of their depth.
Georgallides, Charalambous, Okkarides, Paraskevas, Michail, Elia, Makridis, Nicolau, Okkas, Konstantinou, Aloneftis.
Federico Valentini, Carlo Valentini, Vannucci, Vitaioli, Albani, Fabio Bollini, Andreini, Bugli, Marani, Selva, Bonini.
Alexey Kulbakov (Belarus).