With Judd Trump, Mark Williams, Stephen Maguire and John Higgins all suffering earlier defeats at Berlin's Tempodrom, Allen started as favourite to reach the quarter-finals, but was simply swept aside by a barrage of heavy breaks.
The Northern Irishman won the first frame with a 52, but was forced to sit in his chair and watch as Hawkins seized upon the opportunities that came his way in compiling knocks of 72, 90, 102 and 122 to progress.
World Open holder Allen threw a black towel onto the table at the conclusion of the match, aware that he been well outplayed for large swathes of the evening.
Hawkins's reward is a meeting with Mark Selby or Ding Junhui in the last eight on Friday night. Selby and Ding play their last 16 contest on Friday afternoon.
The 2010 world champion Neil Robertson joined Hawkins in the quarters with a 5-1 win over Andrew Higginson.
Former Welsh Open finalist Higginson won his solitary frame of the evening with a 93 in frame four, but was outplayed by a solid tactical approach from the Melbourne man, who won the other five frames despite running in a high break of 57 in the fifth frame.
Robertson will face the winner of Graeme Dott or Shaun Murphy in the last eight.
Michael Holt continued his decent run of form with a 5-3 win over Kurt Maflin to secure a quarter-final against Anthony Hamilton or Ali Carter.
Holt lost the first two frames, but breaks of 96, 56, 46 and 59 helped him ease through.
Matthew Stevens joined Robertson, Hawkins and Holt in the last eight following a late-finishing 5-4 win over Mark King.
Stevens now plays the winner of the match between Peter Lines and Marco Fu, one of four remaining last-16 ties to be played on Friday, starting at 12pm.
Last 16 results:
Barry Hawkins (Eng) 5-1 Mark Allen (NI)
Neil Robertson (Aus) 5-1 Andrew Higginson (Eng)
Michael Holt (Eng) 5-3 Kurt Maflin (Nor)
Matthew Stevens (Wal) 5-4 Mark King (Eng)
Graeme Dott (Sco) 4-5 Shaun Murphy (Eng)
Peter Lines (Eng) 3-3 Marco Fu (HK)
Ding Junhui (Chn) 3-5 Mark Selby (Eng)
Anthony Hamilton (Eng) 2-5 Ali Carter (Eng)