We report the detection of γ-ray pulsations from the high-magnetic-field rotation-powered pulsar PSR J1119−6127 using data from the Fermi Large Area Telescope. The γ-ray light curve of PSR J1119−6127 shows a single, wide peak offset from the radio peak by 0.43 ± 0.02 in phase. Spectral analysis suggests a power law of index 1.0 ± 0.3 +0.4 −0.2 with an energy cut-off at 0.8 ± 0.2 +2.0 −0.5 GeV. The first uncertainty is statistical and the second is systematic. We discuss the emission models of PSR J1119−6127 and demonstrate that despite the object's high surface magnetic field-near that of magnetars-the field strength and structure in the γ-ray emitting zone are apparently similar to those of typical young pulsars. Additionally, we present upper limits on the γ-ray pulsed emission for the magnetically active PSR J1846−0258 in the supernova remnant Kesteven 75 and two other energetic high-B pulsars, PSRs J1718−3718 and J1734−3333. We explore possible explanations for the non-detection of these three objects, including peculiarities in their emission geometry.