The Argentine, along with sailing partner Cecilia Carranza Saroli, took top spot in the Nacra 17 Mixed Multihull after a dramatic final medal race Tuesday.
The victory caps a difficult year for the oldest sailing competitor at the Games, whose two sons are also representing their country in the 49er skiff class.
Yago and Klaus both swam out to meet Lange, clambering onto the boat to celebrate with their father -- who was clearly touched by the emotion.
After being diagnosed with cancer last year, he used the motivation of his past five Olympic appearances and two bronze medals to ensure he would be ready for the first Olympics to be staged in South America.
"The six months I was dealing with that, I was so positive," Lange told reporters.
"Now when I look back it was a good experience, difficult, but I learned a lot. I was operated on in Barcelona and after five days I was cycling; in a month I was back sailing.
"This may help to give strength to many people who are going through what I've been through. But I prefer to focus on what we did athletically. The disease has nothing to do with it, it was a stone in the road. I became obsessed with getting to Rio very well prepared and we did."
Lange won bronze medals at Athens in 2004 and in Beijing four years later along with teammate Carlos Espinola in the two-person Tornado class, which was replaced by the Nacra on the Olympic program.
He teamed up with Carranza Saroli in 2014.
"This campaign has been fascinating for me," Lange said. "First of all, I never thought I would make a team with a girl, and to make a team with her was fascinating. "And then there's the Nacra, it's a new boat, it's a fascinating boat, so it was very challenging, especially here in Rio.
"I admire a lot the young people and I think we have a lot to learn from them."
Carranza Saroli, 29, is at her third Olympics, having previously competed in the women's Laser radial class at London and Beijing without winning a medal.
"He's a passionate athlete, so it's a pleasure to be a teammate with him," she said of Lange.
"It's contagious how he is so positive about everything."
The Argentines triumphed by just one point overall, finishing sixth in Tuesday's finale after picking up an early penalty which gave their rivals hope -- one place lower and the overnight leaders would've lost gold.
Australia's Jason Waterhouse and Lisa Darmanin placed second to win silver from Austria's Thomas Zajac and Tanja Frank.
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Lange's sons, meanwhile, were seventh overall after 12 races in the 49er skiffs.
In the Finn class, Giles Scott clinched Britain's fifth consecutive Olympic title, following three-time winner Ben Ainslie and his fellow America's Cup sailor Iain Percy.