In a race containing five Olympic champions, it was Jones' dominant run on the third leg that took the Americans to an unassailable advantage.
Jamaica took silver with Russia holding on for bronze as Cathy Freeman closed fast for Australia.
But there was disappointment for Great Britain as a poor start left the team of Natasha Danvers, Donna Fraser, Allison Curbishley to trail home sixth.
Champion
Jones, the Olympic 100m and 200m champion, clocked an unofficial 49.57secs for the third leg.
She handed the baton over to LaTasha Colander-Richardson for the final leg 15 metres ahead of second-placed Jamaica.
Colander-Richardson had only to hold to win - and although Lorraine Graham battled to close the gap the deficit was too great.
The defending champions clocked 3.22:62secs, Jamaica 3:22.25 and Russia 3:23.46.
Jones, her face wreathed in smiles, jogged a victory lap with her team mates Richardson, Jearl Miles-Clark and Monique Hennagan.
Danvers
Danvers was clearly disappointed with her run despite the condolences of her team-mates.
"I feel quite upset," she said.
"What I wanted to achieve just wouldn't happen. I have a responsibility, and I don't feel I lived up to what I expected."
Katharine Merry, who ran a fine anchor leg, disagreed.
"Natasha has no need to be disappointed," she said.
"We are a team and we stick together."