Fox's sister Jessica secured the first two golds in canoe and kayak slalom on the whitewater course, and her younger sibling made it a family affair when she came out on top in a thrilling decider.
Angele Hug took silver for France and British world number one Kimberley Woods took bronze, the first Olympic medals to be handed out in the discipline as it made its debut at the Paris Games.
"I think I’m in shock, I was just so happy to make it through the semi-final, that was my goal, now just go and enjoy it. It's insane, it’s so much fun. Today just went to perfection, I enjoyed every second," Fox told reporters.
In the men's race, top-ranked Briton Joe Clarke had to be content with silver after getting caught up in traffic early on, allowing Kiwi Butcher to move ahead, where he stayed until he crossed the finish line.
"I could feel him all the way down the middle, and he's an absolute powerhouse. I was just going as hard as I could, and I could feel him in the last couple downs (downstream gates)," Butcher explained.
"I just knew that I needed to execute the last upstream, and it would be good as gold."
The 29-year-old was as good as his word, rounding the last upstream gate in a controlled fashion before paddling powerfully to the finish line to become the first men's Olympic champion in the discipline, with Clarke taking the silver.
"An absolute adrenaline dump," he said, describing his feelings as he left the last upstream gate. "I was just looking around, I couldn't believe it. And all my friends on the side, running down with me, was like crazy."
"Shout out to the Aussies. Shout out to the New Zealand team, like they were just running down, so loud beside me, and pushed me to the end," Butcher said, his voice cracking with emotion.
"It's just special to bring this home, it's crazy," he added. "It was crazy. I couldn't even like process any of it, it was pretty special to see the (New Zealand) flag get raised."
Germany's Noah Hegge came third to take the bronze in what was a very successful debut for cross racing, where racers drop into the water together and paddle frenetically through a series of downstream and upstream gates as fast as they can.
Hug's silver aside, it was a disappointing day for the French with Camille Prigent eliminated at the quarter-final stage before teenager Titouan Castryck was sensationally knocked out, despite finishing first in his race.
With the first two in each race going through to the semis, the 19-year-old kayak slalom silver medallist cruised over the line in first place but was bumped down to third after judges decided he failed to pass the third of 10 gates on the course correctly.
