Murphy took a three-frame lead in the first session after racing out of the blocks.
He won the first three frames without Allen scoring a single point, 92-0, 76-0 and 88-0, before taking more evenly fought frames four and five.
The match looked beyond Allen at that point but he remained within touching distance of Murphy when he edged the sixth frame and scored the match's first century by winning 117-5.
The second set saw Murphy pull away again, establishing an 8-4 lead, a frame away from victory. Allen stayed resilient though and took the next two frames to leave the match balanced at 8-6 at the end of the second session.
However Muprhy needed just the first frame of the next session to complete his win.