Former world champion Williams, who beat Sam Baird by the same score in round four, took a scrappy first frame 61-16 before a run of 52 followed by a 39 was enough to secure a two frame advantage.
Bingham, beaten by Ronnie O’Sullivan at the same stage in the world championships, responded well to level things up at two apiece with breaks of 72 and 59.
The ‘Ball-run’ was first to get his hand on the table in the crucial fifth frame but his break of 45 was not enough as Williams cleared with a 74 to put himself within one frame of the semi-final.
Again Bingham was first in but could only make eight. Williams took two visits to confirm his place in the semi-final though with breaks of 29 and 48.
Joining Williams at the semi-final stage is Mark Selby, who overcame Martin Gould 4-3.
Selby made a terrific start with a run of 115 enough to secure the first frame before taking a second, tactical frame 63-55.
Gould levelled matters with runs of 46 and 52 before Selby re-took the lead having prevailed in a tactical exchange to take frame five but Gould pegged back again with a break of 63 to level things up at 3-3.
Selby put together breaks of 38 and 47 to secure the final frame and progression to the semi-final stage.
Elsewhere, Mark Davis went down 4-3 to Gary Wilson while David Gilbert made light work of Stephen Maguire in a 4-1 victory.
Gilbert will face Selby; while Williams will take on Wilson in the semi-finals.
Gary Wilson 4 – 3 Mark Davis
David Gilbert 4 – 1 Stephen Maguire
Mark Selby 4 – 3 Martin Gould
Mark Williams 4 – 2 Stuart Bingham