Andreescu, 18, shook off fatigue and rallied from a break down in the third set to topple the eighth-ranked German, who hasn't won a title since she beat Serena Williams in last year's Wimbledon final for her third Grand Slam crown.
Ranked 60th coming into the tournament, Andreescu will rise to 24th in the world with her first WTA title.
When she finally converted her fourth match point she kissed the sun-baked court and flopped spread-eagled on her back.
- 'It's crazy' -
"If you believe in yourself, anything is possible," Andreescu said as she hoisted the crystal trophy as the youngest player ever to win one of the WTA's prestigious Premier Mandatory tournaments.
"It's crazy. Crazy is the word of the tournament for me. Just crazy."
It's another giant step in a breakout season for Andreescu, who finished 2018 ranked 178th in the world.
She has racked up 28 match wins in 2019 across all levels, including qualifying and challenger circuit wins -- but Sunday's triumph was a cut above.
She had held for 2-1 in the third when she received treatment on her right arm and shoulder and looked to be flagging when she was broken in the fifth game.
Urged by her coach at the changeover to push through, Andreescu dug deep.
"After I spoke to my coach I just let it all out there," she said. "I was really tired, so I went for my shots more, and that obviously worked.
"The next couple games I did the same thing. And I just fought till the end, because physically I wasn't feeling too well. I fought till the end. I managed to pull through."
She broke Kerber in the next game, taking a 15-30 lead with a lovely drop shot-lob combination, and giving herself a break point with an overhead winner before converting with another forehand winner to launch a run of three straight games for a 5-3 lead.
Andreescu had to call on her last reserves as Kerber saved three match points in the next game on the way to earn a break.
But Andreescu broke Kerber for the third time in the set to seal the victory, giving herself a break point with a blistering forehand before Kerber ended things with a ball into the net.
"She did a good job then at the end, especially the last three games," Kerber said.
Andreescu's run to the final included rallying from 3-1 down in the third set to beat Irina-Camelia Begu in the first round and a 6-0, 6-1 rout of former world number one Garbine Muguruza of Spain, with a three-set win over sixth-ranked Elina Svitolina putting her into the title match.
She showed no sign of nerves as she opened the match with a break of Kerber's serve. It would be all she needed to take the set without facing a break point herself.
Kerber's consistency and power from the baseline kept the less predictable Andreescu at bay in the second. The German came up with a massive hold for 2-1, saving two break points before taking a 3-1 lead with her first break of the Andreescu serve and from there forced the decisive set.
Andreescu follows in the footsteps of 2018 champion Naomi Osaka, who won her first WTA title at Indian Wells to launch a stellar season that has seen her capture the US Open and Australian Open titles and rise to number one in the world.
She becomes the fourth unseeded champion after Serena Williams in 1999, Kim Clijsters in 2005 and Osaka.
"Naomi did this last year," Andreescu said. "Now to be able to have my name beside so many amazing champions it means the world to me."