Bol, along with Eugene Omalla, Lieke Klaver and Isaya Klein Ikkink clocked a European record of 3min 07.43sec for victory.
The United States took silver in 3:07.74, with Britain claiming bronze in a national record of 3:08.01.
Bol was timed at a stunning 47.93sec for her final lap, which made up for last year's world championships in Budapest when she fell with the line begging to hand the gold to the US team.
"I hoped to run that fast sometime but in the relay, you never look too much at split times," said Bol.
"It's more about putting it together as a team and technically you have to race it well.
"I just went for it. We just wanted a medal this time, we didn't think it would be gold, just a medal. Well, we got gold and are the Olympic champions. It is absolutely crazy for a small country like ours."
Bol, whose main goal in Paris is winning the women's 400m hurdles, admitted to being spurred on by her dramatic fall in the Hungarian capital.
"Just keep going, keep going," she said of what she was thinking in the final 100 metres.
"And my general anger from Budapest! That and my teammates cheering me. And the atmosphere in this stadium is absolutely incredible. It's crazy. So everything together."
The US quartet comprising Vernon Norwood, Shamier Little, Bryce Deadmon and Kaylyn Brown had led for the entire race.
But everyone at the near-capacity Stade de France knew Brown had to hold off the challenge of Bol, a proven anchor leg runner of the highest quality.
Bol was fourth as she took the baton in her right hand.
Her eye-catching upright running style saw her round the far bend and she started to move up through the gears.
By 200 metres she had gone past Amber Anning of Britain and Belgium's Naomi van den Broeck.
Down the home straight, Brown tried to hold on for a US victory, but just 10 metres from the line the metronomic Bol strode past for a famous victory.
The victory keeps Bol's bid for three Olympic golds on track.
In a quick turnaround, she lines up in round one of the 400m hurdles on Sunday before also tackling the women's 4x400m relay later in the week.
