It wouldn't have to be a single mutation, but let's say intelligence is linear from 1 (apes) to 5 (humans). At some point an animal mutated from 1 to 2, then 2 to 3, etc. Each step the more intelligent version ended up killing off the weaker version (either through violence or just through better survival in nature), and we ended up where we are at 5, which all humans begin at and our surroundings (i.e. nurture not nature) can modify that 5 down to 4.9 or up to 5.1

I'm incredibly not an expert on evolution (it shows I'm sure!), but from a logical point of view that seems like it's feasible at least - whether it's incredibly likely or incredibly unlikely I've no idea.