Bakelants powered away from a six-man late breakaway group with just over one kilometre to go on the 156km hilly ride from Bastia and crossed the line with the bunch breathing down his neck.
Slovakian Peter Sagan finished second and Polish champion Michal Kwiatowski took third place.
"It's the best day of my cycling career," said Bakelants. "It's hard to believe after all the problems I had this year and the previous years.
"I had opportunities earlier in my career but I lacked a bit of luck. I had it today."
It was the first professional win for the 27-year-old, whose previous victory came in 2008 when he claimed the prestigious Tour de l'Avenir.
"This year I had knee surgery and on my comeback at the Tour de Romandie (in April) I suffered from a knee inflammation," Bakelants said.
"I had to quit and could not take part in the Criterium du Dauphine (this month). But after I did well at the Tour du Luxembourg (third overall), the team took a gamble and took me to the Tour."
RadioShack sports director Kim Andersen told reporters Bakelants had often been injured and had made a bad start to the season.
QUIET DAY
"He was happy to be on the Tour and his mission was to win the second or the third stage," Anderson said.
After a chaotic opening day on Saturday, the peloton had a relatively quiet day in Corsica.
There was some excitement as pre-race favorite Chris Froome attacked near the top of the brutal one-km climb to the Cote du Salario, some 12 kms from the finish.
The Briton, however, was caught and finished in the peloton with double champion Alberto Contador who looked fine after taking a tumble on Saturday.
"With that little climb about 10 kms from the finish, I knew the descent was tricky and dangerous. I was on the front with Richie (Porte) and I thought it might be a good time, just to push on a little bit, get ahead and take the descent at my own pace and stay out of trouble," said Froome. "It's always good to keep people on their toes."
The riders also narrowly collided with a small dog on the loose but the pet escaped from the fast-approaching peloton with four kms to go.
German Tony Martin, who started the stage despite suffering concussion, a deep wound to his elbow and grazes in Saturday's mass crash, finished 17:35 off the pace, blood seeping through his back, with several sprint specialists including Mark Cavendish.
Froome's British team mates Ian Stannard and Geraint Thomas, who also crashed in the opening stage, were among the others in the late group.
Monday's third stage offers more action as it takes the peloton through four climbs over 145.5 kms from Ajaccio to Calvi.
