The victory marks only Bingham’s fourth win in ten years at the Masters, and his reward is a match against Wilson - who won six frames on the spin to beat Jack Lisowski earlier on Wednesday.
2015 world champion Bingham has suffered an indifferent 2019-20 season, failing to qualify for the upcoming European or German Masters and exiting the Scottish Open at the first round stage - but put together runs of 50, 76, 86 and 54 to defeat three-time world champion Williams.
It had looked like it would be a fraught and drawn-out affair when the pair went to the interval at two frames apiece but the Ball-run emerged renewed to win all four frames post-interval to claim the win.
“Any victory over Mark, you know, is [great]. He didn’t look at it tonight, but you know I just battled through,” said Bingham in the studio after the match.
“I have been playing well," he added. "I practised well yesterday, I knocked in five tons or so, and I have just been putting the hours in and feeling good.”
Bingham holds his nerve to down Williams
"He's very solid," agreed Eurosport expert Jimmy White.
The first four frames were a bit edgy...after the interval, Bingham was totally in control of the whole match.
Bingham revealed that he had been checking out his statistics at the mid-session interval, and concluded: "I needed to speed it up a little bit, and got my chances, and scored OK."
Earlier on, world number eight Wilson had bounced back from two frames down to take a 6-2 victory.
Lisowski, currently ranked 13th in the world, notched breaks of 56 then 72 in the opening two frames, but Wilson responded with a 66 in the third.
Lisowski then had the opportunity to take the fourth, but missed his shot at the pink, giving Wilson the chance to draw level.
Wilson did not drop another frame - and the only thing that interrupted his charge to the win was a wasp landing on his collar, brushed away by a courageous referee Ben Williams.
Ref fends off wasp attack on Wilson, gets stung for his efforts
"Jack got off to a fantastic start, and I had to be a bit more streetwise towards the end," Wilson told Eurosport afterwards.
I could sense that Jack was starting to get a little bit edgy. It's tough out there - it's the biggest arena we play in.
Eurosport expert Ronnie O'Sullivan suggested that Lisowski needed to improve his temperament on the biggest stages.
"To lose six frames on the bounce, you can't do that - there's something seriously wrong in your game," he said.
Ronnie O’Sullivan chides Jack Lisowski after Kyren Wilson collapse
White concurred - saying that Lisowski had an abundance of natural talent but had to get the right mindset.
"Somewhere along the line, he's got to learn to play the right shots," he added.