Federer needed barely an hour to take his record to 22-3 over Wawrinka, a former world number three who is currently ranked 40th in the world and working his way back in the wake of double knee surgery.
Fourth-seeded Federer, seeking a record sixth Indian Wells title, next faces Britain's Kyle Edmund, a 6-3, 6-3 winner over Macedonian qualifier Radu Albot.
Meanwhile, on the women's side of the draw, Switzerland's Belinda Bencic beat world number one Naomi Osaka 6-3, 6-1 to move into the quarter finals.
She will now face fifth seed KarolínaPlíšková of the Czech Republic.
Member comments