A mixture of missed chances by Ross County and some super saves from Falkirk's Miles Hogarth denied County at least a share of the points as the visitors won 2-0.
Alex Bone missed a couple of sitters for County either side of the interval before Gareth Hutchison gave Falkirk the lead in the 39th minute, side-footing the ball home after David McMahon's cross rebounded off the bar.
County brought on out-of-favour George Shaw in the hope of grabbing an equaliser, but the Bairns clinched the points five minutes from the end when Andy Lawrie forced a ball over the line.