Spontaneous symmetry breaking of relativistic models with O(N)  symmetry results in the emergence of two elementary excitations: the Goldstone modes and the Higgs mode. The massive Higss mode can decay into pairs of Goldstone modes, broadening the spectral line and hence questioning its visibility. Recently a set of scalar response functions was introduced, in which the Higgs mode appears as a well defined peak. We investigate the universal properties of the scalar susceptibility near the quantum critical point in 2+1 dimensions for N=2 and N=3 using Monte Carlo simulation. We demonstrate that the scalar spectral function contains a peak associated with the Higgs mode, which remains well-defined even upon approach to the critical point. We extract properties that characterize the Higgs peak, including the fidelity of the peak and the ratio  ω_H/Δ between the Higgs energy on the ordered side and the single particle gap on the disordered side. The universal nature of these results make them relevant to a broad range of experiments in condensed matter and atomic systems.