The 18-year-old dropped her racket and fell on her back when Kerber hit a backhand into the net on match point to deliver the tournament wildcard the victory.
"It wasn't an easy match. It was one of the toughest matches I've ever played," she said in an on-court interview. "It's so incredible."
Andreescu would love to follow in the footsteps of world number one Naomi Osaka of Japan, who won the tournament last year before claiming the U.S. and Australian Open titles.
"The next is a Grand Slam. Let's see where this can take me," said the unseeded teenager who is ranked 60th in the world but will rise to 24th on Monday.
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"Naomi did this last year. Now to have my name in front of so many champions it means the world to me."
Andreescu played fearlessly at the outset, breaking the former world number one in the opening game of the match and taking the first set.
The eighth seed battled back to claim the second and looked like she would cruise to the finish line when she broke to go up 3-2 in the third after Andreescu needed a medical time out to have her heavily taped right shoulder worked on by a trainer.
Momentum swung in Andreescu's direction when she broke back to level the set at 3-3 and held serve to love in the next game.
Nerves appeared to get to Andreescu near the end, when Kerber saved three match points behind some stout defence.
But Andreescu broke the German in the next game to claim the title and become the youngest woman to win at Indian Wells since 17-year-old Serena Williams in 1999.
"Hopefully this moment can be a great inspiration for many young athletes," she said.
"If you believe in yourself anything is possible. This moment has become a reality so it's really, really crazy."
(Reporting by Rory Carroll; editing by Clare Lovell and Ken Ferris)
