It was 2-2 at the interval but Davis pulled clear when they resumed to set up a semi-final clash with Barry Hawkins.
"I got a great start," Davis told worldsnooker.com. "A 90-odd break in the first frame settled me down early on. I played pretty solid, I don't remember missing too much.
"A couple of the frames went scrappy after the interval, you're never going to have big breaks when they go like that. But I'm very pleased again.
Hawkins sealed his place with a 5-3 win over Matthew Selt, clinching the match with a 102 break.
"I thought the game was pretty good," said Hawkins. "There were a couple of scrappy frames but I definitely cued a bit better today [Saturday].
"I started off like I did yesterday [Friday], I was a bit ropey but as the game progressed I started to get a bit of rhythm and I knocked a few breaks in there in the end."
Peter Ebdon booked a meeting in the last four with Maro Fu following a 5-4 win over Shaun Murphy.
"I'm absolutely delighted to come through another deciding frame match," said Ebdon.
"I tried hard and I was disappointed that I didn't take a couple of chances that I had early on in the final frame although they weren't exactly straight forward. But I got over the line in the end which is what matters.
Fu saw off Stephen Lee 5-1 with a highest break of 99.
"I'm happy to be in the semi-final, I'm still in the tournament. I'm just going to enjoy the occasion it'll be a good game with Peter," said Fu.