Malik Gill's 3-pointer with 1:02 remaining gave Dartmouth a 73-66 lead but the Big Green (1-4) missed the front end of three one-and-ones, giving the Lancers (3-5) an opening.
Shaquille Johnson made four free throws to get Longwood within 73-70. With Longwood pressing, Alex Mitola threw the ball away. Taylor made with a layup and then followed seconds later with the winning free throws. Mitola missed a runner in the lane as time expired.
Johnson hit all 11 of his free throws en route to 18 points.