The 24-year-old beat Ronnie O'Suulivan at the same stage last term before despatching Ryan Day to reach the one table set up. This year he beat Tom Ford in round one but looked to facing a difficult match when Davis took the opening two frames and was 49-0 up in the third. However a break of 81 allowed him to settle and the player from Antrim never looked threatened after that.
He led 11-5 after the second session and finished the match ruthlessly with a breaks of 131 and 101 to serve notice that he is one to watch.
Post match reaction
I just enjoy playing here if you can't enjoy playing in front of packed houses then you dont want to play snooker.
I won the first session 5-3 and the next one 6-2 and obviously won 2-0 tonight but the first session was probably the best I played because of how he played. I don't think Mark Davis will play to many sessions like that and come out behind. I was lucky that I played very, very well and he missed one or two crucial balls. He didn't look like he was going to miss at all, the first two and half frames he was devastating.
I was lucky that he missed on 49 and I made a break of 81 which allowed me to settle and changed things a bit.
It's not just about winning matches, it'a about kicking on in events. As the season has gone on my results have got better. The early part of the season my results weren't great but I've worked hard and the results have got better. My game in general is better, I've always been a good scorer but my all round game is starting to compete with the other top players and that's what you need at this level.
I played for a gap between two reds but didn't quite get it but knew I'd be on the pink. I had another chance later in the match but missed on 73, so if I keep knocking on the door it might happen.
I think if you look at Graeme's results over the last couple of years, it says wonders for how tough mentally he is off the table. It's only been a couple of years since he was looking like provisionally being World No.1 but he's had a few problems off the table but it's good to see him back, he's a great player.
Mark Davis comments
I started off well in going 2-0 up and I should have gone 3-0 but I got a kick when missing on the red ,and from then on he got involved in the game.So looking back it was quite a big turning point even though it was early in the match.
I was cueing well up until that point and to be honest I didn't do a lot wrong, there was a few errors but nothing major.On the whole I thought it was a good session yesterday.
But I'm very disappointed with todays' performance. For some reason my concentration was awful and there is no excuses for that, it's the world championship.
It is hard to way up, because my focus has been great all season, but today I missed too many easy balls, which you cannot do against players like Mark.
I've really enjoyed playing at the Crucible again, but it's frustrating when you dont perform to your full potential.
I had chances in all the first four frames today, but never played, it was a poor performance.
Mark hit the ball great, but I never put him under any pressure out there.So he was able to relax and play his game.
I think he has got every chance of winning the tournament, he has got the game to win it and there is nobody playing any better than him, thats for sure. I hope he wins it.