Surrey have struggled in this competition in recent years given they lose so many players to The Hundred, with 16 in action this season.
And their much-changed side was in trouble early on as Holland and Green reduced them to 43-4.
Ryan Patel, captain for the One-Day Cup, made 53 and put on 68 with Ollie Sykes, who scored 50.
But outside of those, only two others reached double figures. One of those, Josh Blake, was last man out for 31 to give 18-year-old Green his fifth wicket as Surrey left 6.5 overs spare.
Leicestershire, flying high at the top of Division Two in the Championship, were untroubled in the chase, bringing up the 50 in the seventh over and victory was wrapped up by Ben Cox hitting successive sixes in the 30th over to top score with 38 not out.
Pakistan batter Shan Masood even managed to crack a hole in the sunroof of a spectator’s car just beyond the boundary after hitting a huge six.