The American sank a four-foot putt in the second hole of the playoff to beat De Jonge after MacKenzie was eliminated after the first extra hole.
The trio finished on 14-under-par in regulation, with Streb carding a seven-under 63 to catapult himself up the leaderboard on the final day at Sea Island in Georgia.
However, his fourth round got off to a bad start as Streb bogeyed the first, but he responded in style by sinking nine birdies en route to his first win on the Tour.
It was MacKenzie that went into the finale as co-leader - along with Andrew Svoboda - but he failed to build on his round of 65 on Saturday after shooting a modest 68 today.
De Jonge, meanwhile, carded a bogey-free final round to earn himself a spot in the playoff, shooting five birdies in all.