Winfree turbulence is a chaotic wave pattern developing through negative-tension instability of scroll wave filaments in three-dimensional weak excitable media. Here, we investigate the response of Winfree turbulence to a spatiotemporal forcing in the form of a traveling-wave modulation of the medium excitability. It is shown that turbulent waves can be suppressed much more rapidly by this method, in comparison with the space-uniform modulation of the medium excitability. Since the occurrence of Winfree turbulence is currently regarded as one of the possible mechanisms underlying cardiac fibrillation, this method turns out to be suggestive of a possible low-amplitude defibrillation approach.