The 27-year-old from RadioShack - riding his debut Tour de France - was part of a six-man break that formed on the final run into the finish of the lumpy 154km stage from Bastia.
With the peloton closing in, Bakelants surged ahead of his fellow escapees ahead of the kilometre-to-go banner and somehow had the strength to hold off the pack, which was led over the line by Slovakian Peter Sagan of Cannondale, just one second in arrears.
Overnight leader Marcel Kittel (Argos-Shimano) was dropped by the pack on the first of four categorised climbs to pave the way for a debut yellow jersey for Bakelants, who leads Britain’s David Millar (Garmin-Sharp) by one second on GC.
Stage one winner Kittel crossed the line in a large group of riders more than seventeen minutes off the pace after another eventful day on the Mediterranean island of Corsica.
British national champion Mark Cavendish (Omega Pharma-Quick Step) was also part of the second group, alongside a whole host of sprinters whose legs could not cope with the succession of climbs.
Cavendish’s team-mate, the Frenchman Sylvain Chavanel, celebrated his 34th birthday by instigating the final six-man break 10km from the finish.
Jakob Fuglsang (Astana), Gorka Izagirre (Euskaltel), Manuele Mori (Lampre), Juan Antonio Flecha (Vacansoleil) and Bakelants joined Chavanel on the front of the race as the break built up a 10 second lead over the peloton.
The Cannondale team of Sagan led the chase alongside a cluster of riders from Garmin-Sharp, who were hoping to see their man Millar in yellow.
Just as the leaders looked to be crumbling, Bakelants decided to go alone – and defied logic by holding on for the biggest win of his career.
“I’m incredibly happy,” Bakelants told Eurosport. “I’ve never won a professional race before in my career and I’ve had incredible bad luck in the past.
“This year I had an operation on my knee as well which ruled me out of the classics.
“Today we were in a bunch and I can’t win in a bunch so I broke away. We were six riders and we had Sylvain Chavanel, who is good in these situations.
“I pushed it and went on my own. I told myself to give it all I had and have no regrets. I don’t know how tight it was – pretty tight I think.”
After uttering one of the day’s biggest understatements, the ecstatic RadioShack rider added: “I’ve been riding five years for this. The best thing is that it’s only the second day of the Tour and now there is no pressure on me or the team.”
The first half of another stunning stage in Corsica showcased an attacking tour de force from the Europcar team of Thomas Voeckler and Pierre Rolland, both of whom were involved in trademark digs on the succession of picturesque peaks that culminated in the Vizzavona pass, 60km from the finish.
Rolland was rewarded with the polka dot jersey after jumping clear near the summit of the Cat 2 Col de Vizzavona to take maximum points ahead of the peloton.
On the previous climb, the Cat.3 Col de la Serre, Voeckler pinged off the front to test his legs and give the Corsican crowds something to cheer. The 33-year-old veteran was caught just ahead of the summit moments after his team-mate David Veilleux had crossed over in second place behind Blel Kadri of Ag2R-La Mondiale.
Canadian Veilleux and Frenchman Kadri were part of an initial four-man break which formed soon after the start of the stage in the coastal town of Bastia. Also bolstered by Dutchman Lars Boom (Belkin) and Spaniard Ruben Perez (Euskaltel), the quartet built up a maximum lead of just over three minutes ahead of the first climb of the day.
The lead came down to just 55 seconds over the summit of the Cat 3 Col de Bellagranajo before Kadri and Veilleux decided to drop Boom and Perez on the Col de la Serra. Voeckler attacked the pack in pursuit of the leaders and had almost caught team-mate Veilleux when the FDJ-led peloton closed in.
At this point, Kittel and his fellow sprinters had been shed out the back of the pack. Kadri was passed by Rolland near the summit of the Col de Vizzavona after the Europcar leader timed his break to perfection to secure the polka dot jersey.
Rolland’s time at the front of the race was short lived, with the Cannondale team of Sagan leading the chase down the long descent towards Ajaccio.
Race favourite Chris Froome came to the front of the peloton with his Sky team-mates ahead of the final climb of the day, the Cat.3 Cote du Salario, just 13km from the finish.
But it was yet another attack from Europcar – this time Cyril Gautier – which animated the punchy ascent. Gautier was joined by Flecha on the front, but the Spaniard tired, leaving Gautier alone on the front of the race.
Froome laid down an early marker in the GC battle with a late attack near the summit to open up a small gap and remind everyone that he is the man to beat come Paris.
The Kenyan-born Briton sat up soon after the summit as Gautier rode with an eight-second advantage. Once Gautier inevitably succumbed inside the final seven kilometres, the stage was set for the Bakelants break.
A stray dog running onto the road almost wreaked havoc in the chasing peloton – but it was anything but dog days for Bakelants, who pulled off one of the Tour’s great magic acts in holding off the seemingly irrepressible Sagan and the returning peloton.
The Tour continues on Sunday with the third and final stage in Corsica, a picturesque and undulating 145.5km ride along the west coast from Ajaccio to Calvi.