Trump recovered from 6-3 down overnight and held his nerve to produce a break of 53 in the last frame to edge past Thailand’s Thepchaiya Un-Nooh 10-9 at the Crucible in Sheffield.
But Allen was unable to complete an even better comeback against China’s Zhou Yuelong, the Northern Irishman winning five frames in a row from 9-2 down before Zhou won a nerve-racking 17th frame to seal a 10-7 victory.
Trump will face Sheffield-based Ding Junhui in the last 16 in the bottom half of the draw, which has opened up following five-time champion O’Sullivan’s defeat to amateur James Cahill on Tuesday.
However, the 29-year-old Masters champion admits he will need to raise his game against 2016 finalist Ding and was probably one of the only players not happy to see O’Sullivan make an early exit.
“I probably play a little bit better when I play the top players, so hopefully now I can raise my game to how it has been in the Masters or a couple of the other tournaments I’ve won,” Trump said. “All my big titles seem to come when I play Ronnie. I didn’t look at it as a good thing him going out, I always cherish playing him and especially at the Crucible it would have been amazing.
“I need to go back and practice properly, stick four or five hours’ practice in for the next couple of days and come back as a new man hopefully. The way Neil (Robertson) is playing he’s definitely the favourite.
“I’m one of the people that have got a lot to prove here. A lot of the other top players have already won it, so they’ve got that experience, and I’m hopefully going to be able to settle down and really enjoy the game against Ding now.”
Allen trailed 7-2 overnight and lost the first two frames when the match resumed, before breaks of 68, 60, 72 and a total clearance of 131 kept his hopes of equalling the biggest comeback in Crucible history alive.
The left-hander won a scrappy frame to make it 9-7 but Zhou came out on top following a safety battle on the final red and cleared to the pink to set up a last-16 tie against either Jack Lisowski or Ali Carter.
“You can’t be playing the way I played in the first 11 frames and deserve towin a match, it was embarrassing,” Allen said.