McIlroy had finished third, sixth and 20th in his first three events of 2016 before a missed cut in the Honda Classic last week prompted him to switch to a “crosshanded” putting method he last used in 2008.
The 26-year-old needed 33 putts in his opening 71 but just 25 on Friday in carding eight birdies and one bogey to finish eight under par alongside defending champion Dustin Johnson, two behind former world number one Adam Scott.
McIlroy, who single-putted nine of the first 12 greens, told Sky Sports: “I felt like I struck the ball well yesterday, I just did not have the pace on the greens and that’s to be expected when you go to a new grip and are thinking more about technique than speed and feel.
“I did a bit of work on the putting green last night and it paid off today.”
After a birdie on the first was cancelled out by a bogey on the second, McIlroy birdied four holes in a row from the fifth to reach the turn in 32, before saving par from seven and nine feet on the 10th and 11th.
The world number three then birdied the 12th, 15th and 18th to keep Scott firmly in his sights, the Australian carding a 66 in pursuit of back-to-back wins following his victory in the Honda Classic on Sunday.
Speaking about his birdie from 19 feet on the 18th, McIlroy added: “I saw Adam had got to 10 (under) so I did not want to be too far behind going into the weekend. It’s great to see putts like that go in. Those are the putts I have not been holing over the last few months.
“When you see putts go in you do get confidence from that. As the days go by the more comfortable this will become and the more I can think about feel and picking the right line instead of where my hands are on the grip.
“Today I saw a big improvement so I’m very happy.”
Scott was equally pleased after carding eight birdies and two bogeys in his 66, the former Masters champion responding to a dropped shot on the 14th with a hat-trick of birdies.
“I’m very happy,” Scott said. “I got off to a good start again, that’s been the key for me the last few weeks, and then maybe the wind lay down a little on the back nine and allowed me to have the chance for a few more and I hit some good shots and took advantage.”
Asked to explain a run of form which saw him finish second in the Northern Trust Open before winning last week, the world number nine added: “Everything has an effect on another part of the game and all of a sudden as I came to Honda, the swing fell right into place and that’s carried over to the rest of my game.
“That frees up the putting even more, you are in that little closer and can have a run at those 10-footers a little more than the 15 or 20-footers. I would like to keep my swing in this spot for at least the next two days.”
Johnson carded eight birdies in a flawless 64, the lowest score of the week so far, to join McIlroy on eight under, with Danny Willett a shot behind after adding a 69 to his opening 68.
“I’m really happy,” Willett said. “The wind was in a different direction so there were a lot of different shots you had to play. Fortunately the putter is behaving itself nicely and you would take sub-70 round this course four times.”
Paul Casey and Phil Mickelson were three shots further adrift after disappointing ends to their rounds, Casey dropping two shots in the last three holes in a 68 and Mickelson playing his last six holes in four over after four birdies in a row on the front nine had taken him into the lead.
First-round leaders Scott Piercy and Marcus Fraser fared even worse, both shooting 77 to fall nine shots off the pace on one under.
Russell Knox, the sole Scot in the field, is joint-21st after a second 71.
“My tee-to-green game feels good enough to be right up there and in contention but I just have no confidence in my putting, and it’s a shame,” he said.
“Golf is a funny game and I could go out there tomorrow and hole a few birdie putts, and I’m off and running. But right now I stand over the ball and just cannot see it going in.”