Coleman Johnson added 17 points and K.J. Rose 10. Sidibe's double-double was the fourth of his career.
Gilbert scored Fairfield's last seven points of the first half as the Stags took a 35-26 lead. They extended that to 13 with 12:58 left in the game on four straight points by Johnson.
Central Connecticut rallied within two, 55-53, with 3:39 left after Malcolm McMillan's 3-pointer. The Stags immediately rebuilt their lead to 11 points with 1:44 remaining with a nine-point run.
The game was part of the Connecticut 6 Classic being played at Quinnipiac University.