The victory was Na's first since he won the Shriners Hospitals for Children Open in October 2011.
Bubba Watson shot 65 and was among three players at 11 under.
Na said the win this week did more than just get the proverbial monkey off his back - it provides the 34-year-old a great confidence boost.
Kraft's round included a 19-foot birdie putt at 10 and a chip in for birdie from 41 feet at 11.
"This feels unbelievable - I mean, I see the record (of time between wins) every time I'm on TV", Na said. Even though it wasn't for a victory, Snedeker still qualified for the Open as one of the top four finishers who hadn't already qualified. That gave the final spot to Austin Cook.
Kim also set the 72-hole scoring record at 257, finishing with three straight pars to break the mark by one shot. He has one top-10 finish in each of the past two years and won the Australian PGA Championship in 2016.
The only blemish for Kim at the tournament was a double bogey in the second round.
"I'm always up there", said Na, who has 65 career top-10 finishes.
ANP leader Haroon Bilour among 12 killed in Peshawar blast, police say
Local television channels broadcast live scenes of ambulances arriving at the site and rushing victims to the hospital. Bilour's father, Bashir Ahmed Bilour, was killed by a suicide bomber during a meeting in 2012 ahead of the election.
Na turned professional at age 18 in 2001, playing on the European, Asian and Web.com Tours, winning on the latter two, before earning his PGA Tour card in 2004.
Kim tied another Sorenstam record when she was 24 under through 54 holes. In the playoff, Knox hit wedge from 131 yards to almost the same spot on the 18th green, and his long birdie putt curled left to right and into the cup.
DONEGAL, Ireland - Scottish golfer Russell Knox rolled in nearly identical birdie putts from around 40 feet on the 72nd hole and the first playoff hole to win the Irish Open. He would go on to shoot a 66 and finds himself at 14 under.
Na found a fairway bunker at seven and settled for par but resumed his birdie binge with a 43-foot putt at the par-3 eighth, a tap-in birdie after putting his approach at nine inches from the cup and sinking a 23-foot birdie putt to start the back nine.
He sank a five-foot birdie putt at the fourth and one twice as long at the fifth before dropping a 32-footer at the sixth.
Fox had an 8-foot birdie putt to extend the playoff, but it caught the lip and spun away.
"It feels awesome", Na said. First-round leader Webb Simpson, who recorded a 61 on Thursday, slumped to 76-72 on over the final two rounds and finished tied for 47th at 4 under.
Defending champion Xander Schauffele and Kevin Na were at 13 under. He birdied six of the first 10 holes to open up a big lead, and he never looked back, cruising to a final-round 64, 19-under par for the tournament, which was good enough to win the event by five strokes.