Ranked fourth in the post-season tournament, the Rams advance to the semi-finals and will face No. 1 Mount Saint Mary. Game time on Wednesday is 7:30 p.m.
The lone goal for Farmingdale State against Old Westbury came in the 19th minute when Junior midfielder Bryan Argueta of Westbury scored from about 15 yards out.
Rams freshman goalkeeper Justin Silva of Bellrose made six saves to earn the clean sheet.
Farmingdale State and Mount Saint Mary previously met this season on October 15 with MSM winning 3-1.