Selby required little over an hour to reach the first round proper, peaking in the second frame with a rip-roaring 144 total clearance.
Davis, a six-times world champion in the 1980s, was barely able to get on the table but missed out on a chance to pull a frame back in the fourth and final stanza, allowing Selby to come back and finish the job.
The comprehensive victory sets up a tie with Joe Perry in the next round.
Mark Williams and John Higgins also comfortably advanced to the last 32 just after lunchtime on Monday.
Williams, world champion in 2000 and 2003, saw off Liu Chuang 4-1 in the second wave of final preliminary contests. Breaks of 66, 54 and 72 saw the world number seven progress.
And Scotsman Higgins, a four-time ruler of the Crucible, defeated Gareth Allen by the same scoreline. The Scot had a 101 break in the second frame before rounding out the victory with 93 in the final frame.
Williams will meet Robert Milkins in the first round proper while another former world title-holder awaits Higgins, in the form of Ireland's Ken Doherty.
It was not quite so smooth for another Welshman as Matthew Stevens required three frames to finish the job against Alfie Burden.
Having cruised into a 3-0 lead, Stevens then dropped two in a row as Burden launched a respectable fightback, which would prove futile as the former Masters champion finally clinched the 4-2 win to set up a first round tie with Liang Wenbo.
Liang was in ominous form with a 4-1 victory over Ryan Day. The first two frames were shared before Liang reeled off successive breaks of 75, 105 and 72 to advance to a showdown against Stevens.
Ding Junhui saw off the spirited challenge of Thai opponent Dechawat Poomjaeng at the top of the day's play.
The Chinese star began with back-to-back centuries, each worth 107, but failed to shake off Poomjaeng, who won a scrappy third frame. Ding nudged ahead once more, but a 51 dragged Poomjaeng back into the contest again.
The world number nine was not to be denied, however, and moved through to a match against Mark King.
Judd Trump, who has battled with Selby for top spot in the rankings for months, looked to one-up the UK champion by beating Mike Dunn as comprehensively as Selby had defeated Davis.
His 4-0 evening win sets up a first round battle with Dominic Dale, who bested Daniel Wells 4-1 a few feet away on the other table.
Ding Junhui 4-2 Dechawat Poomjaeng
Ryan Day 1-4 Liang Wenbo
Mark Williams 4-1 Liu Chuang
John Higgins 4-1 Gareth Allen
Mark Selby 4-0 Steve Davis
Matthew Stevens 4-2 Alfie Burden
Judd Trump 4-0 Mike Dunn
Dominic Dale 4-1 Daniel Wells