Davis started with a 76 break for the opening frame on his way to a 3-0 lead, with Higgins getting off the mark with a half-ton just before the mid-session interval.
It would be his only frame of the last-16 contest, however, as a Davis run to 52 was followed by a sixth frame won on the colours to claim an impressive scalp.
Higgins, the defending champion after triumph at this event in 2012, joins a number of big names including Judd Trump and Stephen Maguire in failing to reach the business end of the tournament.
Davis will play Xiao Guodong in the quarter-finals after the Chinese player saw off Peter Lines 5-3.
There was an upset elsewhere in the session as Kyren Wilson sent Marco Fu packing with a 5-3 success, hitting an impressive 133 in the process.
Though Fu broke the half-century barrier in all three frames that he won - scoring 50, 71 and 98 - it was not enough to prevent his exit from the tournament.
Wilson meets Michael Holt in the quarters after he followed up on his upset of Trump by outlasting Michael Gould in a dramatic final-frame decider which went to the last six balls - despite Gould hitting two tons at 109 and 127 to lead the match 4-3 from 3-1 down.
China's Ding Junhui caused a mini-shock as he beat Shaun Murphy 5-4 to secure a quarter-final berth. Murphy couldn't build on a century break in the sixth as his opponent took two of the final three frames to secure a last eight match with Neil Robertson who beat Mark King 5-3.
Elsewhere, Mark Selby narrowly avoided an upset after coming from 4-2 down to beat Robert Milkins, clinching a nervy final frame 58-56 to set up a clash with Barry Hawkins who comfortably dispatched of Ryan Day 5-2.
The quarter-finals take place on Friday, with the last four on Saturday ahead of Sunday's final.
Second round results
John Higgins 1-5 Mark Davis
Peter Lines 3-5 Xiao Guodong
Kyren Wilson 5-3 Marco Fu
Martin Gould 4-5 Michael Holt
Mark Selby 5-4 Robert Milkins
Ryan Day 2-5 Barry Hawkins
Shaun Murphy 4-5 Ding Junhui
Mark King 3-5 Neil Robertson