Same word as outdoes:

beat, best, blow out of water, bulldoze, bury, cook, cream, defeat, do in, down, eclipse, exceed, excel, fake out, go one better, leave behind, lick, outclass, outdistance, outfox, outgun, outjockey, outmaneuver, outrival, outshine, outsmart, outstrip, pull a fast one, shake off, shoot ahead, snow, surpass, top, transcend, trash