Mark Williams and Aaron Hill are both through to the last 32 of the German Masters in Berlin.
World number four Allen, who lost out to eventual winner Shaun Murphy in the Masters semi-finals earlier this month, had breaks of 74 and 71 against David Lilley and will now face Wu Yize, who cruised to a 5-1 win against Jackson Page.
In the evening's play, Hill, the world number 59 from Cork, advanced after a 5-2 win over two-time world champion Mark Williams.
Earlier, Ken Doherty was thumped 5-0 by rising Chinese star Si Jiahui in Berlin.
Si made the highest break of the tournament so far with a superb 145 in the fourth frame.
The Dubliner was given little time at the table, with his highest score of 21 coming in the third and frame.
A missed blue in what proved the final frame sealed Doherty's fate as the Chinese player advanced to the next round.
Ricky Walden came through 5-3 against Ryan Day.
Switzerland's Alexander Ursenbacher gave his hopes of retaining his place on the tour a big boost by upsetting Jack Lisowski 5-3 and he will play Ali Carter, tournament winner in 2013 and 2023.
Carter whitewashed China's Hi Guoqiang, while former world champions Mark Selby and Luca Brecel eased into round two with respective 5-2 wins over Liu Hongyu and Jiang Jun.
Three-time UK champion Ding Junhui was thrashed 5-0 by Scotland's Ross Muir.
Elliot Slessor, Yuan Sijun, Anthony McGill, Xiao Guodong, Jimmy Robertson and Daniel Wells all progressed.
Ronnie O'Sullivan and Ding Junhui are among the players who withdrew from the tournament before it begun.
