Bingham will face Ronnie O'Sullivan or Ali Carter in the last eight after getting the better of Hastings potter Davis, who competed well but came up short after returning to the arena for the deciding session this afternoon all square at 8-8 after the opening two sessions.
"It was long old battle and a tough couple of days. I played well in bits and very poor in other bits," said Davis. "I just couldn't pull away. The first session ended 4-4 and I could've probably won it 6-2. I feared another second round exit but I had my little spurt at the right time at 10-10.
"When we were juniors we used to play all the time. This is my 29th tournament and I've entered them all this season. I just love the game and love playing. We've had three weeks off before this and I've been in the gym working with a personal trainer and I feel good.
"I've got nothing to lose now. All eyes are on Ronnie (O'Sullivan) and if it is him I'm playing, it will be a bit more open and will hopefully be a break-building feast."
Bingham was quickly into his stride as a knock of 77 helped him moved 9-8 clear before a clearance of 70 saw the Basildon man pinch the 18th frame after Davis had broken down on 58 when he seemed likelier to level at 9-9.
Davis did not let that dissuade him as he claimed a 19th frame that could have gone either way before a run of 58 saw him restore parity at 10-10.
With the tension palpable, Bingham revelled in the moment as an immaculate knock of 111 earned him an 11-10 advantage after Davis had thrown in a loose safety shot.
Runs of 38 and 57 carried 'Ballrun' to within one frame of the last eight after Davis can only contribute 14 before he dominated the 23rd frame to secure his progress with his practice partner enduring a barren spell at the wrong time in the match.
Davis can reflect upon a fine tournament after ousting John Higgins in the first round while Bingham - the world number eight - extends the best season of his career after winning two of the three events in the Asian Players Tour Championship and remaining unbeaten in snaring the invitational Premier League event.
"Both of us just struggled, I don't know why. I was really expecting something to happen, but it just didn't," said Davis.
"It was very disappointing because I really felt as though I'd be on the verge of doing something if I'd have got through that. Stuart deserved to win, he played a million times better than me and I'm struggling to work out how I won 10 frames."
SECOND SESSION REPORT
Mark Davis and Stuart Bingham finished 8-8 after the second session in the World Championship second round
The opening of the evening session followed much the same pattern as their morning session with Bingham winning the first frame of the evening with a hard-fought break of 54 before Davis immediately pegged him back in a scrappy tenth frame 62-31 to once again level things up.
Bingham pulled ahead again 6-5 and then followed that up with a break of 55 in frame 12 to open up a two frame advantage for the first time in the match.
But Davis then rattled off three frames on the spin to take the lead for the first time going into the final frame of the session.
Bingham, who had a worrying dip in form halfway though their session, dug in to win the final frame 87-6 to ensure that they are all-square going into the deciding session on Monday.
FIRST SESSION REPORT
After an appalling first half of the session and the scores at 2-2, Bingham hit a century but was pegged back again by a determined Davis.
An 82 gave the Basildon potter the lead for a fourth time in the match, but Davis responded with an 84 as the quality of the match improved.
The winner will play either Ronnie O'Sullivan or Ali Carter in the quarter-finals.
The less said about the first two frames, the better. Both players grimaced repeatedly as they missed chances and played poor safety shots.
1996 English Amateur and World Amateur champion Bingham, 36, found his feet with a 67 break to the green after Davis suffered a kick to hand him the chance. Davis dug in with a fairly ugly 57 break to level at 2-2.
After the interval, the play was again sub-standard initially - with pot success down in the mid-seventies - before Bingham came from nowhere to relieve the audience with a 106 break.
He looked set to extend his advantage but an unbelievable miss on a short red let Davis in and he managed a 48 clearance to sneak the frame despite a poor positional shot on the blue. He did well to pot the pink and black.
A flowing 82 put Bingham in front once more and he would have been confident of ending the session two frames to the good - but Davis made it 4-4 with an 84 which, like Bingham's break before, ought to have been a century.
Bingham was 2011 Australian Goldfields Open champion, his only ranking tournament win, and has reached two ranking finals this season - perhaps his best one despite it blowing hot and cold.
Davis, 40, won the non-ranking Benson & Hedges Championship in 2002 and the Six-red World Championship in 2009 and 2012. His best ranking showings have been recent, reaching the last four at the Wuxi Classic, Australian Goldfields Open and UK Championship in 2012.
He shocked four-times champion John Higgins 10-6 in the first round here.