Be/X-ray binary systems exhibit both periodic (Type I) X-ray outbursts and giant (Type II) outbursts, whose origin has remained elusive. We suggest that Type II X-ray outbursts occur when a highly misaligned decretion disk around the Be star becomes eccentric, allowing the compact object companion to capture a large amount of material at periastron. Using 3D smoothed particle hydrodynamics simulations we model the long term evolution of a representative Be/X-ray binary system. We find that periodic (Type I) X-ray outbursts occur when the neutron star is close to periastron for all disk inclinations. Type II outbursts occur for large misalignment angles and are associated with eccentricity growth that occurs on a timescale of about 10 orbital periods. Mass capture from the eccentric decretion disk results in an accretion disk around the neutron star whose estimated viscous time is long enough to explain the extended duration of Type II outbursts. Previous studies suggested that the outbursts are caused by a warped disk but our results suggest that this is not sufficient, the disk must be both highly misaligned and eccentric to initiate a Type II accretion event.