Rahm and Stenson both carded 3-under rounds of 69 on Saturday, while Finau shot 5-under to join the Europeans in the lead at 13-under for the tournament.
Gary Woodland sits alone in fourth at 11-under.
Tiger Woods recorded his second disappointing round of the tournament, shooting even par to fall into dead last at 2-under through three rounds.
The wildest round of the day belonged to Sweden's Alex Noren, whose last five holes consisted of two birdies, an eagle, a triple-bogey, and a hole-in-one en route to a 2-under 70 on the day.
Sunday's final round begins at 10:42 a.m. ET.