St Leonards-based Edhouse ended up losing by three sets to one against the world number one at Alexandra Palace in London on Wednesday night.
But he produced an impressive performance, winning the opening set and leading 2-0 in the third before Price reeled off the final six legs with some top-quality darts.
Edhouse finished an entertaining second-round match with a 95.67 average, having landed four 180s and seven of his 10 attempts at a double.
The 38-year-old was playing in the sport's flagship event for only the second time, but showed no signs of nerves as he clinched the opening set by three legs to nil.
A 106 checkout brought three-time Challenge Tour event winner Edhouse level at 2-2 in the second set before Price held throw in the next leg to level the match at one set each.
The world number 80 was averaging just under 100 as he opened up a 2-0 lead in set three only for Price to roar back and take the set 3-2, sealing it with a 130 checkout on the bullseye.
That proved a pivotal moment as Price went on to claim the fourth set 3-0 - and with it the match - pulling off another 130 outshot to boot. The Welshman ended up averaging 101.28.
Edhouse set up the showdown against Price by recovering from two sets to one down to beat Peter Hudson 3-2 in his first-round match earlier in the evening.
That was a far scrappier affair and in marked contrast to his subsequent performance, Edhouse missed 39 darts at a double before eventually getting over the line.
Fellow local player Rob Cross, meanwhile, will have to wait until just before Christmas to begin his quest to repeat his remarkable title triumph of four years ago.
The number 11 seed will take on Raymond van Barneveld or Lourence Ilagan in round two during the evening session on Thursday December 23.
Dutch five-time world champion Van Barneveld and Filipino thrower Ilagan will meet in round one on Monday December 20. All the action is televised live on Sky Sports.