Winstanley hit seven 180s and averaged 93.66 while also hitting three ton-plus finishes, but all that was only just enough to squeeze by Jones, who averaged even higher at 94 and had four 180s of his own.
Winstanley, from Doncaster, kicked off with a 136 finish in the first leg to go ahead, and hit a 180 in the third to take the set 3-0 and enjoy the perfect start.
A 116 finish started the second set brilliantly for Winstanley as well, and he followed that up with another 136 checkout in the fourth leg, but that was only good enough to level matters, while Jones withstood a 180 from his opponent in the decider to level the match.
Jones really hit his stride in the third set, as he came from a leg down to finish legs of 14, 11 and 15 darts in a fine set as he moved 2-1 up in the game.
Winstanley responded to win the fourth 3-1, finishing double seven and 74 to lead before posting double ten to send the contest into a deciding fifth set.
Winstanley hit 61 to start the final set, and though Jones levelled he took out 24 and 25 as he sealed his place in the second round against Darren Webster.
“That was a really tiring game, I just couldn’t shake Wayne off and every time I tried to do it he just kept coming back at me and back at me,” said Winstanley.
“I thought we both played well, but I really wanted that, I’ve been in a sudden death game before and there’s no way I wanted to play in one again!”
Webster dumped seventh seed Simon Whitlock out with a shock 3-1 victory on Saturday.
Webster did not drop a leg on his way to winning the first set as an out-of-sorts Whitlock struggled to get a foothold in the game.
Whitlock squared the match at 1-1, but Webster upped his game to take the third and fourth averaging more than 94 for the match.
Leeds-born Mark McGrath suffered a nightmare on his debut at the event.
McGrath, who emigrated to New Zealand in 1981, was beaten 4-0 in legs by American Scott Kirchner in a preliminary round match.