Kanayo Obi-Rapu made back-to-back 3-pointers to give Longwood (3-4) its first lead with 2:55 remaining.
But a layup and 3-pointer from Grant Mullins pulled Columbia to within one with 23 seconds left. Mullins came away with a steal on the ensuing possession, and Longwood fouled, sending Alex Rosenberg to the free-throw line with 17 seconds remaining. Rosenberg made both free throws to give Columbia a 69-68 lead.
Shields converted the game-winning layup and the Lions couldn't get a final shot off.
Obi-Rapu made four 3-pointers and finished with 15 points. Leron Fisher had 18 points and eight assists.
Mullins set career highs in makes and attempts from 3 after going 7 of 12. He finished with 23 points, seven rebounds and six assists.