After Vettel made his own stop on Lap 26, the race entered a stage of strategic tension, with Ferrari adamant that Hamilton would have to make a second stop, which would hand Raikkonen back the race lead.
If Lewis Hamilton had to win the United States Grand Prix or even finish in P2, he would have clinched his fifth Formula 1 title today and would be only the third driver in history to win these many championships in the sport's history.
Hamilton, who was fastest in both practice sessions in Austin, needs to outscore Vettel by just eight points to win the championship, and emulate Juan Manuel Fangio with a quintet of titles.
Esteban Ocon was an impressive sixth for Force India ahead of Nico Hulkenberg of Renault, Romain Grosjean of Haas, Charles Leclerc of Sauber and Sergio Perez in the second Force India.
"I didn't really have any problems", he said after the race.
A late pit change while leading the race denied Hamilton a 10th victory of the year as he had to settle for third place at the USA Grand Prix in Austin, Texas. "I don't know why they wouldn't want to win the race, I think they did want to win the race but it just didn't play out the way that we planned".
"That was pretty close and it is always a bit of a shame when you miss out by such a little time", said Vettel.
"That was very important, that was close", said the Briton as he waved at the throng of fans on an overcast and gusty afternoon at the Circuit of the Americas with rainclouds gathering.
"I'm happy we are here and that we win but I think the biggest difference is the way people look at you".
When qualifying began, the two Ferrari men were swiftly setting the pace with Vettel on top early in Q1.
For the seventh time this season, Fernando Alonso was forced to retire.
Another thing to note in the battle between Mercedes and Ferrari is that the red cars had much better straight-line speed in qualifying.
They shadowboxed until Lap 54, when Hamilton attempted to launch a move for second place in the final sector.
Needing to make up ground from his fifth place on the grid, following a three-place grid penalty, he tangled with Ricciardo and spun on the first lap.
Hamilton started from pole, but lost the lead to Raikkonen on the long uphill race to the left-handed first corner.