Fognini, ranked 43rd in the world, notched his first win over eighth-ranked Tsonga in five career meetings.
He also ended the Frenchman's nine-match winning streak that had seen him lift trophies in Rotterdam and Marseille.
Tsonga likely won't be dwelling on the defeat with other matters to capture his attention. His wife is expecting their first child in April and he only decided at the last minute to make the trip to California.
World number one Andy Murray headlined men's second-round play on stadium court, taking on Canadian qualifier Vasek Pospisil.
Murray is making his 12th straight appearance at Indian Wells, where his best performance is a runner-up finish to Rafael Nadal in 2009.
Last year, he exited in the third round, but he will be looking for better with a 12-2 match record in 2017 that includes his 45th career title at Dubai this month.
Swiss third seed Stan Wawrinka, a two-time quarter-finalist, takes a 2-0 career record over Italian Paolo Lorenzi into their stadium-court clash.
In early matches, eighth-seeded Austrian Dominic Thiem eased past France's Jeremy Chardy 6-2, 6-4 while Japanese lucky loser Yoshihito Nishioka upset 19th-seeded Ivo Karlovic 6-4, 6-3.
Nishioka withstood a dozen aces from the Croatian veteran, breaking him three times while saving all seven break points he faced.
Former finalist John Isner of the United States made it safely into the third round with a 7-6 (7/0), 7-6 (8/6) victory over Kazakhstan's Mikhail Kukushkin. And 11th-seeded Belgian David Goffin advanced with a 6-4, 3-6, 6-3 win over Russian Karen Khachanov.
source: news.abs-cbn.com
