The 1995 world championship finalist took a 3-1 lead but Allen fought back to go 5-4 in front before the veteran forced a decider.
It was the Ulsterman who found his game in the crucial frame though, notching up a 69 break to set up a semi-final with Stephen Maguire.
The Scot knocked in two centuries on his way to beating Matthew Stevens 6-4. Maguire raced into a 4-2 lead, with a break of 135 coming in his fourth frame before Stevens levelled up with a couple of tense frames. However Maguire moved to within one of victory with another ton before sealing victory with a break of 83.
Earlier, 19-year-old Yan Bingtao stunned John Higgins 6-3 to reach the semi-finals of the UK Championship on Friday.
Bingtao played a clever game throughout the match and relied on safety and positional play rather than aggressive potting. Bingtao didn't make a single break over 43 as he frustrated Higgins, who was struggling with the table as well.
"I didn't think I was going to win but I was lucky today," Bingtao said afterwards as he followed up his 6-1 thrashing of Neil Robertson in the previous round with another big name scalp.
Higgins, who knocked in century number 774 in his career, now only one behind Stephen Hendry's record of 775, was disappointed with his play, as well as the table saying that "They're probably the tightest pockets I've ever played on as a professional.
"I can't really believe how bad I can be at this game sometimes. The conditions were tough, I knew that by watching the other games. I know that Ronnie and Ding served up a good game but the majority of players were really struggling, it's too tight for me.
"Yan played a good game, he played a really clever game. His safety was really good and he was only taking chances when it was really there."
Bingtao is the first teenager to reach the semi-finals of the UK Championships since Ding in 2005, who he will now face for a place in the final. Ding beat compatriot Liang Wenbo 6-2, knocking in one century break of 101 on his way to victory.