The home side, who sit one spot above bottom-placed San Marino in Group H, struggled to find the breakthrough in the first half, as did the visitors, who have suffered a number of heavy defeats during the campaign.
It was not until the second half that the deadlock was broken through Frunza, who managed to put his side in front following a wave of pressure after the break.
Four minutes later, Sidorenco was able to double his nation's efforts, leaving San Marino with too much to do in order to get back into the game.
With just one minute of normal time remaining, Sidorenco was able to double his efforts and give Moldova three on the night to seal their victory.
Moldova will travel to Montenegro in their final World Cup qualifier on October 15, while San Marino take on Ukraine on the same date.