The RadioShack-Leopard rider formed part of a six-man breakaway group 6km from home and then made a solo bid for glory in the final kilometre.
He looked to have run out of steam and appeared set to be overtaken by the chasing peloton at the death, but hung on to win by a single second from the charging Peter Sagan in second place and Michal Kwiatkowski in third.
Britain's David Millar (Garmin-Sharp) finished in the bunch and is now second overall, but Mark Cavendish's hopes of stage victory were once again dashed after he and former race leader Marcel Kittel (Argos-Shimano) were among the sprinters dropped on the second of the day's four categorised climbs
Chris Froome (Team Sky) gave a glimpse of his fine form with a stinging attack on the final climb of the day, but later sat up and crossed the line safely in the peloton.
The race almost descended back into farce when a dog ran into the path of the peloton 3.5km from the finish, but it managed dash out of the way just in time to avoid a repeat of stage one's late pile-up.
Despite finishing more than nine minutes down and losing the yellow jersey, Kittel claimed two points on the stage's only intermediate sprint to retain the points leader's green jersey, while Pierre Rolland's attack over the category-two Col de Vizzavona saw him move into the mountains classification's polka dot jersey.
Stage two took the riders on a 156km, medium-mountain route from Bastia to Ajaccio, on Corsica's west coast, on a day played out in glorious weather.
A four-man breakaway containing David Veilleux (Europcar), Blel Kadri (Ag2r-La Mondiale), Ruben Perez Moreno (Euskaltel-Euskadi) and Lars Boom (Belkov) went clear straight after the flag, but they were all caught and overtaken on the second and third climbs of the stage.
Europcar duo Thomas Voeckler and Rolland also launched attacks, but they too were unable to stay clear and the thinned-down peloton was together as it approached the day's final ascent, the Cote du Salario, which averages 8.9 per cent in gradient over its 1km distance and arrived 13km from the finish.
Juan Antonio Flecha (Vacansoleil-DCM) and Cyril Gautier (Europcar) saw attacks at the foot of the climb fail, while just short of the summit, Froome darted ahead of the pack with a sudden injection of pace. He was merely giving himself clear road for the descent ahead, though, and soon dropped back into the pack.
A new breakaway group containing Bakelants, Jakob Fuglsang (Astana), Gorka Izaguirre (Euskaltel-Euskadi), Manuele Mori (Lampre-Merida), Sylvain Chavanel (Omega Pharma - Quick-Step) and Flecha formed on the flat run to the finish line and they opened up a gap of 10 seconds.
When that dropped to just five seconds going into the last 1km, Bakelants seized the moment by bursting clear alone and hanging on for the first professional victory of his career.