"I have high expectations going into every week", Johnson said when asked about the U.S. Open.
"I feel like I steadied the ship a little bit after a rough start", said Putnam, who secured his card for the year with his best finish yet.
Johnson opened with a birdie at the 10th.
It was his second PGA Tour win of 2018.
While numerous game's elite are having this week off to prepare for the U.S. Open, Johnson made a decision to play his way into the second major championship of the year at Shinnecock Hills.
If Friday's round is any indication, then it's pretty clear that the world's No. 2 ranked player is more than ready for the season's second major, which he won at Oakmont in 2016.
Johnson birdied the third hole and bogeyed the fifth to make the turn at even par. Putnam also collected seven birdies and a bogey.
"Playing the way I did all week, playing the way I did today (Sunday), knowing everything that was on the line, gives me a lot of confidence going into next week (US Open)".
With a healthy lead and noone able to put pressure on the leader, Johnson recovered from finding trees off the 16th tee to make birdie before holing out from a 169-yards with a nine iron for eagle at the last.
"By the reaction from the crowd, I thought it might have gone in, but I couldn't see it so it was kind of tough", said Johnson after shooting 66.
Putnam, who has never won on the PGA Tour, matched the best round of his short career on Saturday and was delighted talking to the media after his round. "You don't have them very often out here where the hole looks like it's the size of a beach ball and can't miss a putt". He shot a 79 in the first round.
He holed out for eagle from 170 yards on the final hole to seal an emphatic six-stroke victory at the St. Jude Classic.
In a final walkthrough before heading off to Shinnecock Hills and the Open, Dustin Johnson sauntered to a six-stroke victory in the FedEx St. Jude Classic on Sunday to reclaim from Justin Thomas No. 1 in the World Golf Ranking.