The exams are nearly here. Our teacher has covered most of the parts of the syllabus in great detail. But there are some topics he hasn't covered, as well.
and
The exams are nearly here. Our teacher has covered most of the parts of the syllabus in great detail. But there are some topics he hasn't covered as well.
are both acceptable, and the comma is required to show the 'too' sense in the first example, but needs omitting in the second to show the 'hasn't covered them in the same great detail' sense in the second.
With cases like the example in the question, where there is no need to disambiguate, the comma assumes a different role. It is a free choice to include it or not (though there is a tendency towards minimalism). It is now used solely to mark an optional pause in speech. I'd usually include it as that's the way I'd normally read out the sentence.
The only supporting evidence I've found is the final contributor on this Reddit thread.