Daley is one of Britain's most recognisable Olympians after competing at the Beijing Games in 2008 aged 14 and then winning bronze in the 10m platform under intense pressure in his home Games in London in 2012.
While the 22-year-old is better known for his individual exploits, he and 19-year-old Goodfellow were fancied to win a synchro medal after taking European silver in May.
They were the last pair to dive in the open-air Maria Lenk Aquatics Centre, meaning they knew what they needed to do to overhaul Germany's former world champions Patrick Hausding and Sascha Klein with their final effort.
With a score of over 84 points needed, the British duo waited anxiously before leaping into the pool in celebration when the score of 89.64 came up.
"Going into the last round there's an intense pressure in any competition, but when it's the Olympics it multiplies by a million," said Daley.
Goodfellow added: "I was nervous. But when we first started we knew there would be pressure. And we knew we'd be the last divers to go.
"We just kept our nerve and stayed in the moment."
British pair keep composure
Daley and Goodfellow, who moved in with his older team-mate as a lodger before the Games, put themselves in medal contention from their first dive.
They were joint third in the standings after round one, remaining in the bronze medal position following their second and third dives.
A loose dive saw them drop to fifth after round four, but they moved back into third before the final round with a forward four-and-a-half-somersault dive described by BBC Sport expert Leon Taylor at the time as their "best of the day".
But they trumped that with their final effort, keeping their composure to secure a sixth-round score only bettered by the Chinese and Americans.
Chinese domination continues
Chinese pair Lin and Chen have dominated the synchro event since linking up last year, winning the World Championship, World Cup and four World Series events.
And they showed why with another masterful display on their Olympic debut together.
Lin, 25, and Chen, 20, led from the opening round, winning with a total of 496.98 points ahead of Boudia and Johnson (457.11) and Daley and Goodfellow (444.45).
Their victory was China's fourth consecutive Olympic gold in the event and maintains the country's hopes of a clean sweep of the eight diving events in Rio.
'Well done lads!' - social media reaction
And he always knew it would happen…
Watch a spikey-haired 14-year-old Tom Daley tell the BBC's Gabby Logan in 2008 that diving from the 10m platform was "like doing loop-the-loops on a rollercoaster" and he was "scared" the first time he jumped from the 10m platform.