The second half mirrored the first, with the home side dictating the tempo. Substitute Joe Gormley nearly doubled the advantage in the 55th minute, only for McCarey to make an acrobatic save.
Moments later, the Reds' all-time top scorer was again denied, this time by the crossbar.
McCarey continued his inspired form, brilliantly parrying Curran's powerful half-volley in the 66th minute to keep his side in the contest.
Niall Currie will be disappointed that his charges struggled to create clear opportunities throughout the 90 minutes, although they will be frustrated that they did not leave north Belfast with a point.
Their best chance for an equaliser came in stoppage time when Michael Newberry was dispossessed on the edge of the area.
However, Cliftonville's stopper David Odumosu was equal to Steven McCullough's curling effort, ensuring the Reds clinched all three points.