Three-times world champion Drysdale, 29 faded in the last 500m when he had the gold in his sights. He had come into the race with questions over his fitness, after being hit with a stomach bug early in the week.
He recovered well enough from his post-race medical trauma to take pale-faced part in the medal ceremony, half an hour after the finish.
He won the first New Zealand medal of the Games when cut back to third after storming to the front in the third 500m.
Defending champion Olaf Tufte of Norway, then Czech Ondrej Synek overhauled him in the shadow of the finish line.
Drysdale had barely qualified due to his illness, his semifinal time relegating him to the unfamiliar territory of lane six.
He trailed fast-starting Alan Campbell early, rowing through the opening 500m in fourth place, 1.01sec off the lead set by the flying Briton.
At the 1000m, he was still fourth, now 1.75secs behind new leader Tufte, but made a huge move to carve out a 1.61sec lead at the 1500m.
Tufte, who won bronze behind Drysdale at the last world championships, came back to win in six minutes 59.83 seconds. Synek clocked 7min 00.63sec and Drysdale 7min 01.56sec.
Drysdale held up the start of the race, when he pointed out to there was "a lot of weed" in his lane.
A boat carrying officials cleared the obstruction.
In the women's pair New Zealand's 2005 world champions Juliette Haigh and Nicky Coles finished fifth in 7min 28.8sec, behind defending champions Georgeta Andrunache and Viorica Susanu of Romania, who won in 7min 20.60sec.
You Wu and Yulan Gao of China were second in 7min 22.28sec, and world champions Yuliya Bichyk and Natallia Helakh of Belarus third in 7min 22.91sec.
