David connected on 8-of-13 shots from the field and Rayshawn Goins supplied 14 points and 13 rebounds as the third-seeded Dukes (20-14) advanced to their first NCAA Tournament since 1994.
Andre Nation put in 10 points for James Madison, which will be appearing its fifth national event overall.
The top-seeded Huskies (20-12), meanwhile, were seeking their first NCAA berth since 1991.
They were led by Jonathan Lee with 14 points.
2014: The Year in Music [PHOTOS]