Backstrom posted a 1-under 70 in the final round at Aa St. Omer Golf Club to finish regulation at 4-under-par 280 alongside Dwyer, who shot a 68. Both players returned to the par-4 first to begin the extra session where Backstrom ultimately prevailed with a par for his maiden title.
Backstrom was two shots back to start the day and he struggled early with a bogey at the par-3 second. He countered with a birdie at the par-4 third but suffered a bogey at the par-3 fourth and dropped another shot with a bogey at the par-4 sixth.
The Swede made a move around the turn, however, with back-to-back birdies from the par-5 ninth. He climbed to 4 under with a birdie at the par-4 12th but found trouble with a bogey at the par-3 17th.
Backstrom responded with a birdie at the last to force the playoff that gave way to an exemption on the European Tour in 2006.
'This means the world to me,' said Backstrom. 'Now I can prepare properly for every event and I think that's massive in this sport because you have to use everything you can to your advantage.'
Dwyer had a strong front nine with a pair of birdies to make the turn at 3 under. He jumped to minus-4 with a birdie at the 12th but struggled to a bogey at the par-5 14th. The Englishman came back with a birdie at the 17th.
James Heath picked up a birdie at the par-5 14th that moved him two shots clear of the field at 6 under. Heath, who held the outright lead heading into the weekend, let the opportunity slip at the par-4 15th and walked off with a double-bogey.
The 22-year-old dropped another shot at the last to finish one shot out of the playoff after a round of 72. Heath was joined by Michael Jonzon and Steven Jeppesen at 3-under-par 281.
Carl Suneson and Ross Fisher shared the 54-hole lead but both players struggled with matching rounds of 74 on Sunday. They fell back into a tie for sixth place with Ben Mason, James Hepworth and Alvaro Salto at 2-under-par 282.