The Englishman had battled back from two over on day one to pick up nine shots in ten holes and lead by four in difficult conditions at Augusta National.
That lead had evaporated inside 12 holes of round two despite conditions being more favourable, with Rose sitting at three over for the day.
He had spoken on Thursday evening of how pleased he was to have kept his head after a slow start, and his mental toughness shone through for a second consecutive day as he picked up three birdies to get back to seven under after a 72.
American Tony Finau and Austrian Bernd Wiesberger both fired rounds of 66 to sit at four under alongside World Number Two Justin Thomas, another American in Cameron Champ, South Korean Si Woo Kim and Japan's Hideki Matsuyama.
Rose has an excellent record at Augusta, with two runner up finishes and just one missed cut in his previous 15 appearances, and he revealed he went into match play mode on the back nine to keep his nose in front.
"I was joking, the finger was heading towards the panic button a little bit," he said.
"I had a little talk with myself on eight and said 'you're still leading the Masters', and I just changed my mindset a little bit and started to play match play against the golf course.
"I scratched a line on my scorecard and told myself I was three down and could I go ahead and beat the golf course from that point on. I had a putt on 18 to win my match one up but unfortunately it just slipped by. But an honourable draw.
“It was a tough start today, poor tee shot on number one and had to chip out sideways, and then from that moment on, for the first six or seven holes I just kept leaving the ball on the greens but in really tough spots.
Didn’t hit the panic button and really pleased to turn it around
“I felt like I really hung in well and weathered that period of the round. Just little things were going wrong but didn’t hit the panic button and really pleased to turn it around."
After having to play out sideways on the first, Rose picked the shot back up on the par five second but things continued to go awry on the front nine.
He failed to find the green with a putt from over the back of the par three fourth, three putted the sixth and failed to get up and down from the sand on the seventh.
A Leishman birdie on the 13th had him in a share of the lead and the winner of the 2016 Nedbank Golf Challenge had the solo advantage with another gain on the 15th.
But Rose also took advantage of the par five 13th as he got down in two from 40 feet, before holing from 23 feet on the next to get his nose back in front.
A tee shot to 19 feet on the 16th then put him two ahead before Harman and Zalatoris set about closing the gap.
Zalatoris finished his round with three birdies in a 68, while Harman made gains on the 17th and 18th in a 69.
Leishman carded a 67 and Spieth a 68 as he made three birdies in his final six holes.
Wiesberger made seven birdies with a single dropped shot, while Finau carded an eagle, six birdies and two bogeys.