Vettel was just.061 seconds behind.
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.
Vettel has to win the remaining three races this season to have a chance of becoming world champion this year. If Hamilton wins, Vettel must finish no longer than second to keep the championship alive next week into the Mexican Grand Prix. A fifth career title would tie the British driver with Argentina's Juan Manuel Fangio for the second-most championships in Formula One history.
That saved Hamilton 10 seconds over a stop under racing conditions and he was on Raikkonen's tail within eight laps.
Hamilton refused to get into predictions about Sunday's outcome.
"I knew it was edgy between us on my last run, but my second lap was just that little bit getter and that enabled me to pull it out".
Belgian Stoffel Vandoorne qualified last but will move up the grid thanks to engine penalties applied to the Toro Rossos of Pierre Gasly and Brendon Hartley, who will go to the back of the field.
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"Collectively as a team we didn't perform that great today - and that's not something we usually do", said Hamilton.
The four-time champion German said his relationship with the defending champion had always been respectful, despite their lifestyle differences. He has also won five out of six races held so far in Austin. Vettel has one victory and missed the podium three times in that span. He at least knows his vehicle has the muscle to compete with Mercedes again.
I'll have to see what happened with the strategy.
It took him until Lap 51 to get within one second of Verstappen and gain DRS, but the Dutchman was likewise closely tailing Raikkonen in the lead, neutralizing the advantage.
Mercedes Team Principal Toto Wolff said this week he could use team orders to help protect Hamilton to win the title.
The championship leader trimmed his time while, behind him, Max Verstappen's session was ended when his right rear suspension appeared to fail after he ran across the "sausage" kerbs at Turn 17.