The Spaniard, who was given the all-clear to race after a medical on Thursday, lapped the twisting Circuit of the Americas in a time of one minute 38.343 seconds, just 0.028 ahead of McLaren's Jenson Button.
Heikki Kovalainen, the Finn who is replacing compatriot Kimi Raikkonen at Lotus for the last two races after the 2007 champion pulled out to have back surgery, was 13th fastest with a time just 0.249 seconds slower than team mate Romain Grosjean.
Teams and drivers were kept waiting for 40 minutes as heavy fog shrouded the circuit carved out of the south Texas scrubland.
Formula One's governing body, the FIA, said the delay was necessary because medical helicopters would not be able to take off or land if needed.
When it did eventually start, the session was soon red flagged again with officials waiting for the absent helicopters to land.
After the fog burned off, the sun came out and Alonso - who hurt his back when he hit a kerb at high speed during the previous race in Abu Dhabi - quickly went to the top of the timesheets.
Red Bull's world champion Sebastian Vettel was well down the list, ending the session in 18th place.
The German, who clinched his fourth consecutive drivers' title last month and started from pole in Texas last year, can add another line to the record books by becoming the first Formula One driver to chalk up eight successive victories in a single season with a win on Sunday.
Britain's Lewis Hamilton, winner of the inaugural race in Austin last year, was also slightly off the early pace clocking the sixth best time ahead of Ferrari's Felipe Massa and Red Bull's Mark Webber.
Russian Daniil Kvyat made his first appearance for Toro Rosso at a race weekend and was 17th fastest with a lap only 0.202 slower than Australian race regular Daniel Ricciardo, the man he is replacing next season.
American Alexander Rossi, the reserve driver, also had a run in the Caterham and posted a quicker time than the team's French race driver Charles Pic.
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