Attempting to win a modern day record seventh title, the 36-year-old from Essex beat the New Zealand professional, Dene O'Kane, 10-3.
O'Kane finished the morning's first session still in touch at only 5-3 down but his resistance was finally broken in second session.
The 31-year-old London-based Aucklander trailed by 42 points with one red remaining, but then managed to manoeuvre Davis into conceding a seven-point penalty.
He cleared the balls to force the second finish on a re-spotted black of the match. Luck then deserted him and Davis's length-of-the-table pot secured a 6-3 advantage. With the pressure off, Davis then proceeded to show the form that has brought him two major titles and the leadership of the provisional world rankings.
He took the 10th frame with a break of 48 and added his best of the match, a run of 95, in the 11th. There was no way back for O'Kane, the world No 22, as Davis completed an unbroken sequence of frame victories, taking the 12th 64-21 and the 13th 76-31.
'The two re-spots were crucial, particularly the one this morning in the seventh frame,' Davis said. 'It could easily have been 4-4 after the first session and even though I was 5-3 up, I wasn't in a good frame of mind.' Davis now meets the Cannock professional, Steve James, in the last 16.
Alan McManus finally beat Fergal O'Brien after surviving the latest comeback of the tournament, turning his 6-3 overnight lead into a 10-7 victory.
At one stage the world No 6 from Scotland was one ball from a 10-3 success but later O'Brien, the world No 50, fought back to within one ball from trailing 9-8.
During the 11th frame, McManus achieved his highest professional break of 143, a clearance that has been bettered by only four players in The Crucible's history - Cliff Thorburn and Jimmy White with 147, Doug Mountjoy (145) and Davis (144). It surpassed Thorburn's 139 in pursuit of the pounds 15,400 high- break bonus in this year's championship.
Gary Ponting's world championship adventure ended in disappointment nine months and 10 matches after starting out in the Blackpool qualifiers. The 19-year old first-season professional from Bristol lost 10-2 to Willie Thorne, who said: 'I felt embarrassed for the kid.'
Results, Sporting Digest, page 43