The country's other three finalists missed the podium.
Emma Twigg suffered the anguish of finishing fourth in consecutive Games as she looked to prove herself after a study sabbatical last year.
Her ninth season in the elite single sculls boat ended in desperation, 2.94s adrift of Australian rival Kim Brennan.
Her fortitude to return failed to gain an elusive disc as American Genevra Stone and China's Jingli Duan kept her out of the frame.
The women's eight of Emma Dyke, Genevieve Behrent, Kerri Gowler, Grace Prendergast, Kelsey Bevan, Ruby Tew, Rebecca Scown, Kayla Pratt and coxswain Francie Turner finished fourth in New Zealand's maiden appearance in the discipline at a Games. The United States won with Britain second and Romania third.
The men's eight of Stephen Jones, Brook Robertson, Alex Kennedy, Jonathan Wright, Isaac Grainger, Shaun Kirkham, Michael Brake, Tom Murray and coxswain Caleb Shepherd finished sixth in a final won by Britain.
Drysdale has fashioned a crème de la crème Olympic career, regardless of his pursuit for gold medals at consecutive Games. He becomes the 12th New Zealander to achieve that feat.
"I must've have just got in front with a couple of strokes left when I threw in a couple of short ones," Drysdale said.
"I spent a lot of energy getting into the lead and I thought that was enough. But I knew I had to stack it in close to the line.
"Usually after I win I don't feel the pain, but today... I felt the pain."
Drysdale also paid tribute to his training partners, double scullers Zoe Stevenson and Eve Macfarlane, who bowed out in the semifinals, and his coach Dick Tonks.
"I couldn't do it without them. It was sad to see them go out but great to get a 'team medal'.
"There was a lot riding on this one. This year there were a couple of dark days where you realise you don't recover as well as you get older, but I enjoyed the last three months."
Drysdale was the oldest of the country's nine champions at London, and arguably the athlete with the most to consider when contemplating four further years of toil. In addition, he is a five-time world champion, a victor at numerous global boutique events and a Beijing bronze medallist. He had little more to achieve in the sport, yet sought an opportunity to crown his legacy.
Drysdale says he'll never forget the uncertainty felt while floating next to Martin in the finish area at Rodrigo de Freitas lagoon.
"We were looking at each other, looking at the board, just waiting, waiting, waiting," he told NZ Newswire.
"I'd come here to win and my whole four years were resting on this one final bit. "It's not the way you want to do it but I'll take a gold medal any day."
"It was a super human effort from Damir, he just closed me down so quickly," Drysdale said. "I looked across and I thought he might have even got ahead of me at one point."
"It's something I haven't really tried but I just thought 'whack in as many as you can on the surge' and that's what it came down to."
Drysdale was favourite ahead of Beijing and London as defending world champion. This time he had earned silver behind Czech Ondrej Synek at the last two pinnacle events. Synek finished third in Rio.
At London, Drysdale hit the front in the third 500m and held off Synek.
In Rio, he repeated the exercise against Martin, but the Croat fought back.
Drysdale's career has been punctuated with injury and illness.
He suffered a different type of setback in December when coach Dick Tonks was cut from the Rowing New Zealand ranks for mentoring overseas athletes without permission. A deal eventually allowed Tonks to maintain ties with Drysdale until Rio, but not without considerable stress and angst.
Tonks, in his employment with the governing body since 1999, has secured six Olympic golds, including at least one at every Games during that period.
Despite his bouts with adversity, Drysdale was already a great Olympian. Success in Rio has only gilded his reputation.
New Zealand's oldest Olympic champions
Mahe Drysdale, 37y 8m 25d, 2016, rowing, single sculls
Chris Timms, 37y 4m 15d, 1984, sailing, Tornado
Ian Ferguson, 36y 2m 10d, 1988, canoeing, K2 500m
Blyth Tait, 35y 2m 16d, 1996, equestrian, eventing
Helmer Pedersen, 34y 6m 25d, 1964, sailing, Flying Dutchman
Eric Murray, 34y 3m 5d, 2016, rowing, coxless pair
