The Bristolian went down 5-4 to Anthony Hamilton with the Nottingham potter sealing a place in the last 16 with a 57 break in the deciding frame.
World number 37 Hamilton led 3-1 and 4-2 before being pegged back but kept his composure to book a contest against Allister Carter.
Earlier Michael Holt defeated Williams for the second time in four days to reach the last 16.
Holt got the better of the former world champion in the one-frame Shoot Out tournament on Sunday, but proved the win was hardly a fluke with a dominant 5-1 success in Berlin.
The world number 28 started in supreme fashion by storming to the top of the high break charts with a 144 total clearance, and though Williams responded with a 94 break, it would be the Welshman’s only frame of the contest.
Holt continued to look assured in his break building and capitalised on numerous unforced errors from the out-of-sorts Williams to set up a meeting with Kurt Maflin.
Mark King made a 105 break against last year’s runner-up Maguire as the world number six suffered an embarrassing 5-0 whitewash.
Higgins went down 5-3 to Peter Lines on Wednesday in one of 10 last 64 matches held over to the Tempodrom venue in Berlin.
But world number one Mark Selby joined Shaun Murphy, Neil Robertson and Ding Junhui in the latter stages of 2013's first ranking event.
Peter Lines recovered from trailing 2-0 and 3-1 to complete a 5-3 win over Ken Doherty in the final match of the last 32 stage.
He will face Marco Fu in the last eight on Friday afternoon.
Last 32 Results:
Anthony Hamilton 5-4 Judd Trump
Graeme Dott 5-3 Dave Harold
Shaun Murphy 5-3 Robert Milkins
Mark Selby 5-2 Joe Perry
Ding Junhui 5-0 Marcus Campbell
Marco Fu 5-3 Ricky Walden
Mark Allen 5-2 Dominic Dale
Michael Holt 5-1 Mark Williams
Neil Robertson 5-1 Michael Wasley
Mark King 5-0 Stephen Maguire
Kurt Maflin 5-4 Xiao Guodong
Barry Hawkins 5-2 Dechawat Poomjaeng
Allister Carter 5-3 Fraser Patrick
Matthew Stevens 5-1 Jamie Burnett
Andrew Higginson 5-1 Stuart Bingham
Peter Lines 5-3 Ken Doherty