Kirk, who won his second PGA Tour title at the McGladrey Classic in November, judged the break perfectly as he completed a five-under-par 65 to post a 12-under total of 198 at Waialae Country Club in Honolulu.
That left him one ahead of fellow Americans Harris English (67) and PGA Tour rookie Will Wilcox, who fired a joint best-of-the day 64 to surge into contention in the first full-field event of the year on the U.S. circuit.
While Masters champion Adam Scott surprisingly failed to mount his expected charge after being ideally placed just three strokes off the pace overnight, the fans at Waialae were treated to a slugfest at the top of the leaderboard.
Twelve players held at least a share of the lead during Saturday's wildly fluctuating third round before Kirk broke clear with his timely birdie on the 18th green.
"It definitely breaks more than it looks but I remembered having that putt before ... and thankfully it went in," Kirk told Golf Channel of his curling birdie putt.
Though conditions were favourable for low scoring on a calm morning at Waialae before the breeze picked up a bit in the afternoon, Kirk readily admitted he got the most out of his round.
"A few good breaks for me and holes where I missed the fairways, but got decent lies in the rough and guessed the flyers just right," the 28-year-old American said after mixing six birdies with one bogey.
"That's tough to do out here."
Wilcox, who secured his card for the 2013-14 PGA Tour via the lower-tier Web.com Tour last year, realized he was finally living out his dream career as he birdied the last two holes.
"Walking down 18, me and my caddie looked at each other and I was kind of having to pinch myself," said the 27-year-old from Birmingham, Alabama. "This is a dream come true to be able to play out here, it's pretty cool.
"I felt pretty good coming down 18. It's nice to play well and make the first cut in a season I get to play," added Wilcox, who is making only his third career start on the PGA Tour.
Australian world number two Scott, the highest-ranked player in the field, birdied his opening hole to close briefly within two of the lead but his momentum then stalled as he went on to bogey the sixth, 16th and 17th.
Though Scott comfortably birdied the last after reaching the green in two and two-putting, he carded a one-over 71 to finish the round six strokes off the lead.
American Zach Johnson, who clinched his 11th PGA Tour title at the Hyundai Tournament of Champions in Kapalua on Monday, fired a six-birdie 66 to end the day at nine under, just three off the pace.
Level with Johnson were his compatriots Jeff Overton (65), Pat Perez (66) and overnight leader Brian Stuard (71), South African Retief Goosen (66), Japan's Hideto Tanihara (70) and Australian Robert Allenby (65).
Johnson is aiming to join South African Ernie Els as only the second player to win the Sony Open and Hyundai Tournament of Champions in the same season. Els achieved the feat in 2003.
Tee times were brought forward by two-and-a-half hours for Saturday's third round due to a forecast for poor weather later in the day.