Bunting stole the first leg in a race to two sets and went on to win five legs in a row, with just one more needed to whitewash the defending champion.
Throwing for the match, Bunting got up and running quickly and had three darts in hand with 67 left, but one dart at double 16 went astray and that would be as close as he came.
Humphries still had work to do in the deciding leg of set two but threw a maximum to leave 50 before taking that out in two darts after Bunting had fallen well short in his attempt to hit 140 for the win.
Taking the lead for the first time in the match by bossing the opening leg of the deciding set, Humphries was kept honest by Bunting but by now had things under control as the pressure returned to Bunting, throwing to survive.
Both men wasted their first three darts but after Bunting made the same mistake twice, Humphries opened with 152, followed it with 120, and needed just two darts to take out 70 in clinical fashion for the comeback win.
Humphries will face Ricardo Pietreczko in round two after the German beat Raymond van Barneveld 2-1.
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