The 24-year-old American fired a sparkling seven-under-par 65, matching the lowest score of the week, after battling to a 73 in the previous round.
"It was a very good round," Kim told reporters after covering the back nine at Augusta National in five-under 31 to finish at 12-under 276, four shots behind the triumphant Phil Mickelson.
"I was happy that I hung in there and gave myself an opportunity today where if I shot something silly low, I would have a chance to win this golf tournament.
"I was very frustrated, just because I feel like I'm doing all the right things," Kim added, referring to his wayward driving in Saturday's third round.
"I feel like my swing is coming along and I get out there and I still can't find the fairway. It was very frustrating yesterday but I was happy at least get it around at one over because I felt like it could be quite a few strokes over par."
Extra jolt Kim clinched his third PGA Tour title in a playoff at last week's Houston Open and he felt that gave him an extra jolt of momentum for the opening major of the year.
"I definitely gained a lot of confidence after last week," he said. "The attitude I had, the mindset I was in last week, really helped me this week.
"I've gotten over a little hump in my golf career when I felt like things were stalling. If I can just get my ball striking to where it was, I'm going to be at a different level." Kim began Sunday's final round seven strokes off the lead and vaulted into contention with an electrifying birdie-birdie-eagle-birdie run from the 13th.
His sizzling burst ended when he rammed in a 25-foot uphill birdie putt at the par-three 16th to lie one off the pace at 12 under.
Asked if he had a particular target in mind, he replied: "I really didn't. I knew I was coming from pretty far back and Phil's obviously playing great.
"I just tried to make as many birdies as possible and fire at a couple flags. I grinded, I hung in there and I'm proud of the way I stuck it out."