The world number three carded a one under par 70 to reach three under par one shot behind defending champion Jordan Spieth who struggled around in two over 74.
“It’s up there,” said Rory about his efforts in difficult blustery conditions.
“I kept my composure and I played the shots when I needed to.
“It’s only the second day, there’s still two days to go, but it’s a great round and it’s nice to be up there near the lead going into the weekend here instead of on the cut line and having to battle back where I found myself the last couple years. I’m happy with where I’m at.”
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The 26-year-old, who closed with rounds of 68 and 66 last year and has a scoring average of 68.5 on the weekend in 2014 and 2015, added: “If I can have a weekend like I did that last weekend, I’d be very happy.
“Obviously with the position I was in last year going into the weekend, there wasn’t much pressure.
“You could go out there and free-wheel it a little bit and try to make as many birdies as you could and the conditions were more benign, so you could go after the course a bit more.
“But I’ve played this golf course well on the weekend the last couple years, and I have to take confidence from that.
“Hopefully it’s a third year in a row and a third weekend in a row where I can post a couple of good scores and see where that leaves me at the end of the week.”
Ireland’s Shane Lowry blamed mental errors for a second round of 76 which dropped him down the leaderboard on a testing second day of the Masters.
Lowry carded three birdies, five bogeys and a double bogey on the 12th for a halfway total of 144, although that was still good enough for a place inside the top 10.
“It was tough,” said Lowry, who was joint second overnight after an opening 68.
“I didn’t do myself any favours with the start I got off to, which was just purely a mental error on the first and second and all of a sudden I have two bogeys on the card.
“I felt like I fought really hard today and I was really disappointed to bogey the last because if I had been standing here one under I would have been really happy.
“I am still in a decent spot for the weekend depending on what the leaders do.
“You have to be mentally strong and tough and I managed to keep my head on quite well today and play some golf.
“(I am) A little disappointed with 76 but the two round total is good. It’s up to me to do what I can tomorrow and give myself half a chance for Sunday.”
Speaking about his double bogey on the 12th, the 29-year-old added: “I just tugged the tee shot on 12 and ended up in a bush. I dropped it in the bush and just got it out and then got up and down for five.
“It was actually a decent five in the end - there is no way I wanted to go back to that tee!
“There is an 80 out there today without doing much wrong. You have to fight and grind for every par and that is what I did today.”
Meanwhile, former champion Ian Woosnam has called time on his playing career at the Masters, 25 years after winning the green jacket at Augusta National.
Woosnam added an 81 to his opening 82 to finish 19 over par.
“That’s my last go. I am not fit enough to play with my bad back,” he said.