The 2005 world champion led 6-3 after the first session, and then rattled off four frames in a row to reach the final - finishing in style with a 104.
Murphy will await the winner of Ronnie O’Sullivan v Neil Robertson, with that semi-final taking place on Saturday, live on Eurosport and the Eurosport Player.
Shaun Murphy ‘takes advantage’ of Mark Allen’s bad luck
O'Sullivan lifts Shanghai title for third successive year
Allen took the first frame before Murphy reeled off three in a row with breaks of 51, 88 and 82.
Shaun Murphy punishes another Mark Allen miss
The pair both scored 74 in the next two frames as Murphy kept his nose in front, and he stretched that advantage by winning the final two frames of the first session.
Murphy then raced through the second session, as breaks of 64, 80, 61 and finally 104 wrapped up an impressive win.
He goes on to face either defending champion O’Sullivan or Robertson in Sunday's final.
O'Sullivan clinches dramatic comeback win over Wilson in Shanghai
O’Sullivan produced a remarkable comeback to beat Kyren Wilson on Thursday, battling back from 5-1 down to win 6-5.
Robertson meanwhile enjoyed a comfortable 6-2 victory over Barry Hawkins to book his spot in the last four.
Shaun Murphy 10-3 Mark Allen
Ronnie O’Sullivan v Neil Robertson
O’Sullivan wins third consecutive Shanghai Masters
O'Sullivan knocks in second ton against Murphy