Jones twice went ahead with breaks of 68 and 42 but very sportingly owned up to a double-hit on a pink in frame four while building another run. From there Higgins made it 2-2 with 43 heading into the mid-session interval.
And the four-time former world champion was on another level from there, starting the post-break frames with a crack at a maximum break thwarted only by an unfortunate kiss while potting his 10th red-black combination.
The 80 was followed by a 95 and a 70 as the Scot narrowly missed out on a century break on each occasion but ultimately booked his place in the last-16, where Ryan Day awaits after edging out Martin Gould in a last-frame decider.
A nine-frame epic was the last thing on anyone’s mind when Day took the tournament’s highest-break record from Matthew Stevens with a monster 137 clearance to go 3-0 ahead.
But ‘The Pinner Potter’ picked up an important and morale-boosting pre-intermission frame with a break of 72 before coming back out and keeping the momentum going, eventually making it three apiece with a knock of 71.
It appeared that an incredible comeback was on the cards when Gould made it four in a row, but another Day century was followed by a collection of mini-breaks to seal a thrilling win.
Judd Trump also found himself three frames down in his round-of-32 encounter with Australian Goldfields Open winner Barry Hawkins before coming back to win 5-3.
Despite a 52 break after going a frame down, Trump failed to take his chances and seal the second, ultimately going further behind to a 27 clearance after Hawkins had pegged him back.
Two became three courtesy of a run to 51 before the Bristolian took his first frame on the final colours for a glimmer of hope heading into the break.
A post-interval whitewash from Trump took in runs to 58, 63 and 77 and turned the match on its head before ‘Ace’ ground out the win in frame eight.
Mark Allen is next up for the 23-year-old in Thursday’s second round.
And Graeme Dott advanced by knocking out wild-card qualifier Jin Long 5-2 to set up a meeting with Stephen Lee, who defeated Marcus Campbell in the previous session.
Breaks of 62 and 56 helped Dott surge into the third 3-0 lead of the afternoon session only for Long to take the next two.
Resisting the same comeback which knocked Hawkins out and almost did the same to Day, Dott regained control and took the next two to march on.