JR Inman's 3-pointer put Rutgers up 69-66 with 3:35 left, but DePaul responded by scoring the next seven. Burns made a pair of free throws, Tucker hit a 3-pointer from the top of the key and Mac Koshwal made two free throws to give DePaul a 73-69 lead with 2:12 left.
The Blue Demons never trailed again.
Jaron Griffin's basket got the Scarlet Knights within 73-71 with 1:43 left, but Tucker made 1-of-2 free throws and Rutgers center Hamady Ndiaye missed the front end of a 1-in-1.
Koshwal scored 18 points for DePaul (8-9, 4-2 Big East).
Rutgers (8-11, 0-6 Big East) lost its sixth straight game.
Inman finished with 22 points and eight rebounds and Anthony Farmer added 17 points.
Tied at 18, Rutgers outscored DePaul 16-2 midway through the first half to take a 34-20 lead on Corey Chandler's basket. Mike Coburn's 3-pointer extended Rutgers lead to 37-22 with 6:17 left in the half. DePaul was able to cut the Rutgers lead to 45-32 at the half on back-to-back baskets from Matija Poscic. Poscic finished with 10 points.