Former world champions Higgins and Robertson overcame Liang Wenbo and Marcus Campbell respectively in the round of 16 on Sunday morning, both by a score of four frames to two.
And Trump, who moved top of the world rankings with victory at the recent International Championship tournament, saw off Dave Harold 4-1 to advance into the last eight.
In other round five results from the Princess Hotel in Sofia, Tom Ford downed Jack Lisowski 4-1 to set up a quarter-final meeting with Mark Davis, 4-2 conqueror of Thepchaiya Un-Nooh.
Rory McLeod beat Li Yan 4-1, while Ben Woollaston recorded 4-1 win over Jamie Cope and Andrew Higginson wrapped up a 4-2 success over Anthony McGill.
In quarter-final action later in the day, Trump continued to gather strong momentum with a 4-0 sweep of Higginson highlighted by an effortless 119 break.
Davis defeated Ford 4-2 to make himself next in line for the in-form Bristolian in the last four, while Higgins' whitewash of McLeod and Robertson's 4-2 triumph over Woolaston sets up a mouth-watering other semi-final between the two former Crucible kingpins.
Round Five results:
Jack Lisowski 1-4 Tom Ford
Li Yan 1-4 Rory McLeod
Thepchaiya Un-Nooh 2-4 Mark Davis
Dave Harold 1-4 Judd Trump
Andrew Higginson 4-2 Anthony McGill
John Higgins 4-2 Liang Wenbo
Jamie Cope 1-4 Ben Woollaston
Marcus Campbell 2-4 Neil Robertson
Tom Ford 2-4 Mark Davis
Judd Trump 4-0 Andrew Higginson
John Higgins 4-0 Rory McLeod
Ben Woollaston 2-4 Neil Robertson