The world number one - winner in 2008 and 2010 when the invitational event was staged at Wembley Arena - dominated the deciding frame after trailing 5-1 to secure a meeting with Mark Williams in the last eight on Friday night.
Selby is renowned for his fighting qualities having recovered from trailing 9-6 to defeat Ronnie O'Sullivan 10-9 in the 2010 final. He came from 4-0 down to overcome Neil Robertson 6-4 on his way to winning the UK Championship last month, but this win was every bit as impressive.
"I don't know how I've come through that game," said Selby. "Stuart was playing fantastically well so I couldn't really complain if I lost 6-1 or 6-2 because he punished me every time I made a mistake. I sat there and tried to relax and thought if I could pinch one or two frames, you never know. When I got back to 5-3, I knew I was in with a chance.
"He started missing a few, and I started to capitalise myself. It is a huge tournament for me, and you still want to be involved.
"I won twice at Wembley Arena, but as a snooker venue I think it was too big. It held 15,000 people, but we only used 2,500 of that so a lot of the atmosphere got lost, but here it is a lot more compact."
The stats before this match suggested it was going to be a close call with Selby leading 8-7 in their career meetings, but Bingham was fresh from giving his opponent a 6-0 beating in the Premier League, an event he holds.
Selby opened up with a neat 63 in snaring the opening frame, but was largely reduced to a watching brief as Basildon's Bingham responded with 30, 40, 55 and 78 to lead 3-1 at the mid-session interval.
In contrast to the turgid affair between Williams and Matthew Stevens earlier in the day, Bingham was relishing his surroundings as a rapid 86 saw him move 4-1 clear.
The sixth frame lasted 42 minutes and went around 30 minutes without a ball being potted.
Bingham compiled 55, but had to wait until the colours to win it as a safety error by Selby saw his opponent clear from green to pink for a 5-1 advantage, but the 'Jester from Leicester' was far from finished.
A run of 57 saw Selby halt the bleeding to trail 5-2 before he managed to leave Bingham in his chair in the eighth frame rounded off by a 45.
Bingham looked to be heading for the winning post when he slammed a long red down a hole early in the ninth frame, but missing a red to a middle bag proved so costly with Selby recovering in making 86 to win a third straight frame in closing to 5-4 behind.
It was now game on as a 68 from Selby forced the deciding frame after Bingham broke down on eight in failing to hole a red to a middle pocket. Bingham failed to come up with the several snookers he needed with the tension clearly affecting Bingham more than Selby.
Bingham would miss a red in the final frame to a middle hole that finally ended his hopes, but one could hardly argue with the composed nature in which Selby completed the win.
"He got going, and I started missing a few," said Bingham. "Every frame is different. I won five frames, he won five frames. I'm going to stay positive. I loved the occasion.
"I was in my element leading 5-1 and cruising. I will take it as a kick up the backside. I was ten times better than him at 5-1, but he was ten times better than me coming back. It is just one of those things.
"Mark is known for coming back. Good luck to him."