Straka, who is chasing his first win on the US PGA Tour, finished with five birdies at the Innisbrook Golf and Spa resort in Florida.
Johnson, Watson and Jim Furyk are tied for 11th and still well within striking distance after opening with a two-under 69.
"I played a little bit better than my score," Johnson said. "But first time being here in a while, not real used to the golf course. It was a good score."
Like Straka, Dahmen has yet to win on the Tour. He rolled in six birdies and just one bogey. He is coming of a tie for 12th at The Players.
American Dahmen already had a top 10 finish this season when he tied for ninth at the Farmers two months ago.
Straka's best finish of the season was a tie for 13th at the same event.
Knox had one of the more entertaining rounds by making an albatross on the par-five 11th after taking a double bogey two holes earlier.
"It's a good way to go from plus two to minus one very quickly," Knox said. "Didn't even have to putt, which was great."
Defending champion Paul Casey opened with a 70, while Jon Rahm made his tournament debut with an even-par 71.
Early tee times didn't help Reed, who had a 77, or Day at 74.