WordNet sense 1 (overcome, as with emotions or perceptual stimuli):

overpower, overtake, overwhelm, whelm, sweep over

WordNet sense 2 (get on top of; deal with successfully):

master, subdue, surmount, get over

WordNet sense 3 (win a victory over):

defeat, get the better of

WordNet sense 4 (overcome, usually through no fault or weakness of the person that is overcome):

get the best, have the best