The world number six is strongly fancied to lift the trophy in Sheffield this year and clinched a crushing 13-4 win over China’s Ding Junhui.
Resuming with a 12-4 lead after dominating the first two sessions of the match, Bristol-born Trump made a break of 66 to complete his day’s work by mid-morning.
He faces Ronnie O’Sullivan or Stuart Bingham next. They were due to resume their quarter-final this afternoon, with Bingham holding a surprise 5-3 lead, a scoreline that meant for the first time in this tournament O’Sullivan was no longer the bookmakers’ title favourite, with Trump assuming that mantle.
Trump was runner-up at the Crucible in 2011, and also reached the last four in 2013, while his victory at the recent World Grand Prix set him up ideally for a tilt at glory on snooker’s most prestigious stage.
But while Trump believes the snooker he played in building a 6-0 lead over Ding on Tuesday was tournament-winning form, he has also been troubled by illness this week.
“I felt ill before the game so I was a bit worried about how I was going to play and how my concentration was going to be,” Trump said.
“It was a bit iffy in the middle of the match, I missed a few and got quite tired. I haven’t been sleeping that well so I just need to go and rest up now for the next game.
“It’s just a bit of a fever I think, a bit of a cold. I just don’t feel too great. I’ll just go and rest up now and I should be fine for tomorrow.
“I just shut him out which I wanted to do, and put a lot of pressure on him from the start. When someone goes 6-0 up against you you’re under extreme pressure and every ball seems hard then.
“If I play like I did then, I won’t get beaten, but to keep that up for another five days is going to be extremely hard.”
Trump, 25, vowed he would not use illness as an excuse should he not land his first World Championship title.
He added: “When you get to the semi-final the crowd will be immense so that will pick me up anyway and I’ll completely forget about everything.”
It was confirmed by World Snooker that O’Sullivan will face no punishment over Tuesday’s curious incident involving his chalk.
Five-time champion O’Sullivan - who earlier in the tournament played some of a frame in his socks and was then warned about his behaviour following a hand gesture in the second-round match against Matthew Stevens - caused a stir when he placed the small cube of chalk on the baize while lining up a shot.
It is deemed to be against competition rules if any object is used to measure gaps or distances, and therefore subject to a foul with a seven-point deduction.
However, referee Terry Camilleri failed to call the penalty, and a tournament spokesman said that was the end of the matter, with no prospect of retrospective action.
Asked for his own view of what O’Sullivan did, Trump said: “I don’t think he knew what he was doing, I didn’t have a clue about the rules either so I don’t really think it was anyone’s fault.”