We consider families of sparse Laurent polynomials f1, . . . , fn with a finite set of common zeros Z f in the torus Tn = (C − {0})n. The global residue assigns to every Laurent polynomial g the sum of its Grothendieck residues over Z f . We present a new symbolic algorithm for computing the global residue as a rational function of the coefficients of the fi when the Newton polytopes of the fi are full-dimensional. Our results have consequences in sparse polynomial interpolation and lattice point enumeration in Minkowski sums of polytopes.