Drysdale made his move in the third 500m, overtaking early pacesetter Martin as the pair left Ondrej Synek in their wake and battled for gold.
The Kiwi, who won the same event in London four years ago, took an almost boat-length lead at one point before Martin pushed back and looked to have got over Drysdale in the final stretch. However, Drysdale put in a couple of big strokes to the line, winning by the narrowest of margins.
“That was absolutely amazing,” Drysdale said. “It could have gone either way.”
He timed his big push perfectly. Incredible finish.