The Masters champion has not ventured beyond the second round in Sheffield on his six previous visits.
Twice he has fallen at the first hurdle, while in the last four years Allen has been knocked out in the second round.
But last night he completed a 13-8 victory over Cambridge’s Joe Perry – who caused the shock of the tournament by beating defending champion Mark Selby on the opening day – to secure a last-eight meeting with either Kyren Wilson or Jamie Jones. Their match resumes this morning, with Wilson leading 5-3 in their best-of-25 contest.
If 26-year-old Wilson does progress, it will be a repeat of January’s Masters final, when 32-year-old Allen came through 10-7 to pocket the £200,000 winner’s prize.
Allen – who only clinched his top-16 spot to secure a Crucible ticket at last month’s China Open – saw his 5-3 advantage wiped out in the morning session, as Perry restored parity at 8-8.
But the Northern Ireland potter – whose best Crucible showing came in 2009 when he reached the semi-finals – won the first four frames of the evening, thanks to breaks of 133 and 74, before wrapping victory up with a clearance of 122.
Ronnie O’Sullivan must come from behind to beat Ali Carter when the pair resume their second-round match this afternoon, trailing 9-7.
O’Sullivan, who beat Carter in the final in both 2008 and 2012, is seeking a sixth Crucible title.
However, he went into the second session of their best-of-25-frame contest 5-3 down and his chances of progress were not helped as he lost the first three frames.
Although O’Sullivan ended the poor run by winning the next two, he was far from his fluent best and Carter made him pay with a break of 51 to go 9-5 ahead.
However, O’Sullivan finished with a flourish, as breaks of 79 and 105 saw him reduce the deficit to two frames again.
The pair resume on Saturday afternoon.
Earlier, 20-year-old Lyu Haotian – who is based in Sheffield at Victoria Snooker Academy – hit back from an 8-3 deficit to trail world No 6 Barry Hawkins 9-7.
Leading 5-3 after the first session, Hawkins increased his advantage to 8-3 with breaks of 124, 83 and 61.
But Lyu, the youngest player competing in Sheffield who beat Marco Fu in the first round on his Crucible debut, refused to buckle, winning the next four frames with breaks of 125, 72, 79 and 60.
Hawkins, though, ensured he would resume today with an advantage, potting the yellow and green to lead 9-7.