Ricky Werenski got to 10 under but bogeyed No. 18 to finish with a 68.
A two-time victor on the Web.com Tour, Putnam birdied No. 18 to tie up Johnson once again after a bogey-free round.
"I feel like I steadied the ship a little bit after a rough start", he said.
Preparing for the US Open starting later this week, Johnson launched his claim for the Classic title early with a par on the first hole, while playing partner Putnam made a double-bogey. Johnson turned in the lowest score under par by a victor here since David Toms at 20 under in 2003 - before the course was redesigned dropping par from 71 to 70 after the 2004 tournament.
Johnson, 33, lost top spot in the world rankings to compatriot Justin Thomas, who is not taking part in the tournament.
Johnson's final shot on the 18th hole was the final impressive shot in a tournament full of him.
For those who are, in fact, looking for reasons to bet against him, here's all we've got: No one has ever won the U.S. Open a week after winning a PGA Tour event. Now he will play in the last group on the final day for the first time on the PGA Tour with Johnson.
"I knew coming in this week that I was swinging really well and had a lot of confidence in my game".
Topping his walk-off eagle won't be easy.
Dustin Johnson plays his shot from the second tee during the final round of the Fed Ex St. Jude Classic at TPC Southwind in Memphis Tennessee
"It's tough to get the ball on the green if you don't drive it in the fairway", Mickelson said.
Watch the incredible shot below.
J.B. Holmes had five birdies and two bogeys for a final round 67 to end in third place.
Austin Cook (65), South Africa's Retief Goosen (66), Chris Kirk (69), Trey Mullinax (70), Brandt Snedeker (70) and Chez Reavie (71) tied for sixth at 7 under.
It appears on paper as a one-sided battle but tournament golf works in unusual ways and Putnam is an emerging star with two victories on the Web.Com Tour prior to graduation to the bigger stage this year. Teeing off in the afternoon when the wind was stronger, Nordqvist closed her bogey-free round with a birdie on the par-5 ninth.
Johnson and Putnam were tied for the lead at 15 under after the third round and were five strokes clear of the rest of the field.
Johnson hit an iron 307 yards off the tee at No. 10.
Lehman eagled the par-5 eighth and played a 10-hole stretch in 7 under before dropping a stroke on the par-4 18th. Johnson then hit his approach to 3 feet for his second birdie to go 16 under.
NOTES: Johnson was the first on tour to win by holing out from off the green since Jordan Spieth at the 2017 Travelers Championship.
Nice wheels: Kim Jong-un admires Trump's presidential vehicle
According to Will Ripley, CNN correspondent who has visited North Korea 19 times, the interpreter with President Trump is Dr. Top leader of the Democratic People's Republic of Korea (DPRK) Kim Jong Un (L) shakes hands with U.S.