We present broadband spectral energy distributions (SEDs) and light curves of the gamma-ray binary 1FGL J1018.6−5856 measured in the X-ray and the gamma-ray bands. We find that the orbital modulation in the low-energy gamma-ray band is similar to that in the X-ray band, suggesting a common spectral component. However, above a GeV the orbital light curve changes significantly. We suggest that the GeV band contains significant flux from a pulsar magnetosphere, while the X-ray to TeV light curves are dominated by synchrotron and Compton emission from an intrabinary shock (IBS). We find that a simple one-zone model is inadequate to explain the IBS emission, but that beamed Synchrotron-self Compton radiation from adiabatically accelerated plasma in the shocked pulsar wind can reproduce the complex multiband light curves, including the variable X-ray spike coincident with the gamma-ray maximum. The model requires inclination ∼50• and orbital eccentricity ∼0.35, consistent with the limited constraints from existing optical observations. This picture motivates searches for pulsations from the energetic young pulsar powering the wind shock.