Trump trailed Barry Hawkins 3-0 in the first round before battling back to win and the left-hander recovered from a similar position against Northern Ireland's Mark Allen.
Allen took the opening two frames but Trump found his form with a century in the third and took the next two as well.
Trump was in first in the sixth frame but ran out of position and Allen eventually worked a chance to level the scores, only to miss a straightforward yellow.
It looked as though he may have got lucky when the white ran up close to a red, but Trump pulled off a superb thin cut with the rest and went on to win the frame and take the match in the next.
Earlier in the day, Ali Carter found the form which took him to the World Championship final in May as he crushed Stephen Maguire 5-0.
Maguire was Carter's victim in the semi-finals at the Crucible and the English potter sank the Scot again, this time firing a 120 break on the way.
"I gave Stephen the utmost respect today [Thursday] and it was just a match where everything went my way," Carter said.
"He only potted one ball in the first four frames."
The 33-year-old Essex potter is fighting an ongoing battle with Crohn's disease, and is managing the condition by keeping to a diet free of wheat and dairy products.
That helped him go all the way to the world final, where Ronnie O'Sullivan was his conqueror, and has saved his career, with Carter having given thought to retirement at the end of last year.
Carter told worldsnooker.com: "When my health was not right I felt as if I was fighting two battles - one on the table and one off it. But I am feeling fit now thanks to the diet and as long as I stay healthy I will continue playing."
Carter will face Scotland's John Higgins in the quarter-finals after Higgins thrashed Ryan Day 5-0.
Mark Williams also advanced to the last eight with a 5-2 victory over England's Ricky Walden, who triumphed in Shanghai in 2008.
And the Welshman will face Joe Perry in the quarter-finals after the Englishman surprisingly hammered 2010 world champion Neil Robertson 5-0.
The pair practise together in Cambridge and Perry got the better of the Australian in fine style.
"Sometimes the game just doesn't go your way and that happened to Neil today [Thursday]," Perry said.
Stuart Bingham beat Jamie Cope 5-1 in an all-English tussle while Graeme Dott beat Stephen Lee by the same scoreline and Shaun Murphy beat Mark King 5-3.