In a session cut to under an hour because of fog and then an errant medical helicopter, the two-time world champion showed few ill effects from his high-speed ride across the kerbs at the Yas Marina Circuit in Abu Dhabi 12 days ago.
Jenson Button was second fastest for McLaren ahead of Valtteri Bottas of Williams and Esteban Gutierrez of Sauber with the two Mercedes of Nico Rosberg and Lewis Hamilton fifth and sixth.
Newly-crowned four-time world champion Sebastian Vettel was down in 18th place for Red Bull on a strangely chaotic day of frustration for most drivers, the teams and the spectators at the Circuit of the Americas.
Alonso's success was the first in the opening free practice session at a Grand Prix since the Belgian Grand Prix in August.
Heikki Kovalainen, replacing compatriot, Ferrari-bound Kimi Raikkonen at Lotus for the final two races, was a respectable 13th, only 0.249 seconds down on his team-mate Romain Grosjean.