The Higgs mode associated with the amplitude fluctuation of an order parameter can decay into other low-energy bosonic modes, which renders the Higgs mode usually unstable in condensed matter systems. Here, the authors propose a mechanism to stabilize the Higgs mode in anisotropic quantum magnets. They show that magnetic anisotropy gaps out the Goldstone magnon mode and stabilizes the Higgs mode near a quantum critical point. The results are supported by three independent approaches: a bond-operator method, field theory, and quantum Monte Carlo simulation with analytic continuation.