World number eight Bingham led the last 16 clash on four occasions at The Crucible Theatre in Sheffield this morning (Sunday), but each time St Leonards-based Davis pegged him back.
Essex cueman Bingham, a 10-2 victor over qualifier Sam Baird in round one, took the opener 76-38 after Davis’s hopes of getting back into the frame were ended by a tricky missed red along the bottom cushion.
But world number 16 Davis, who pulled off a magnificent 10-6 win over four-time champion John Higgins in the previous round, restored parity by clinching a second frame spanning more than three-quarters-of-an-hour 79-40.
Bingham took the third 73-17 thanks to a break of 67 only for 40-year-old Davis - the reigning Six Reds World Champion - to make it 2-2 at the interval by clinching the fourth 69-17 with a run of 57.
After the resumption, Bingham again got his nose in front as a break of 106 - the only century of the match so far - gave him the fifth frame 115-4. He then looked like winning the sixth after opening up a 40-point lead, but Davis came back to pinch it 63-55 for 3-3.
Although Bingham hit an 82 to pocket the seventh 96-1, once again he was unable to establish a two-frame cushion because Davis claimed the eighth 84-3 with all his points coming in one visit. His highest break of the match so far featured an excellent red to the middle with the white tight to the bottom cushion.
The players will come back at 7pm this evening for eight more frames with the final session scheduled for 1pm tomorrow. Davis is bidding for a place in the quarter-finals of the sport’s blue riband event for the first time having previously got to the last 16 in 1995 and 2010.