Smith and Starks hit a pair of free throws each in the final 16 seconds and junior Mikael Hopkins contributed nine points and eight rebounds off the bench as Georgetown (6-2) used its interior strength to win its fifth straight. Senior Nate Lubick added 10 points.
Colgate (4-3) entered with the best 3-point marksmanship in the nation (51 percent), but missed its first eight perimeter attempts and fell behind 10-0 before sophomore Austin Tillotson made a 3-pointer with 10:58 left in the first half on his way to a game-high 21 points.
The man-to-man defense of the Hoyas compensated for their own shooting woes. Georgetown hit only 37.5 percent from the floor, missing their first nine 3-point attempts.
Colgate cut the Georgetown lead to four points before the Hoyas scored 20 points on their first 10 possessions of the second half to take a 41-27 lead. The 20-10 run featured an ice-breaking 3-pointer, from sophomore guard D'Vauntes Smith-Rivers, and 3-point-plays in the paint from Smith and junior guard Jabril Trawick.
Midway through the second half, Colgate reeled off nine straight points to cut into Georgetown's biggest lead, 14 points. Senior forward Murphy Burnatowski hit a 3-pointer and junior guard Damon Sherman-Newsom added a backcourt steal and a layup as Colgate sliced the deficit to 43-38.
The Raiders pulled closer when Tillotson found junior guard Luke Roh on a backdoor cut to make it 56-52 with 39 seconds left. But Colgate would get no closer as the Hoyas made five of their final six attempts from the free throw line.
Burnatowski contributed 12 points and a game-high 10 rebounds, but hit only 1 of 8 attempts from beyond the arc. The Raiders finished 5 of 24 on 3-pointers (20.8 percent).
Georgetown's inside strength was key. The Hoyas out-rebounded the Raiders 42-33 with Lubick and Smith-Rivera getting seven each and the 6-11, 350-pound Smith added five.
It was Georgetown's eight win in nine meetings with Colgate.