Ding and Higgins had both won their opening matches of the tournament with ease, with the former recording a whitewash against Robert Milkins and the latter easing past Fergal O'Brien 5-2.
However, their round of 16 ties proved to be their last at the tournament, as the Chinese star was beaten 5-2 by Scott Donaldson and the Scotsman was defeated by Thepchaiya Un-Nooh 5-4, having led 4-2 in the best of nine clash.
Neil Robertson thrashes Zhou Yuelong to claim European Masters title
Meanwhile, Williams failed to progress from his first-round tie against Yuelong Zhou, who recovered from a 4-3 deficit to win the final two frames.
In the late match Mark Selby was at one stage trailing Barry Hawkins 4-0 but he produced an epic comeback to draw level at 4-4.
However Hawkins kept his composure in the decider and progressed to the next round.
Elsewhere among the big names, Neil Robertson recorded a straightforward victory over Graeme Dott, racing into a 3-0 lead and closing it out 5-2. He will face Un-Nooh in the quarter-finals.
Ali Carter, meanwhile, will take on Donaldson in the last eight after seeing off Michael Holt 5-4.
Finally, in the last first-round ties, Gary Wilson and Zhao Xintong will meet after beating Luca Brecel and Michael White 5-1 and 5-2 respectively.
Robertson in emphatic march to semi-finals, Zhou knocks out Hawkins
Thepchaiya Un-Nooh makes a 146 at the European Masters