Scheffler, who has performed well in majors and in the Ryder Cup but hasn't won on the PGA Tour, was closer to the cut line than the lead until he ran off five straight birdies, the last one a 35-foot putt on the par-3 eighth.
He finished with a par for a 64 and wound up within two shots of the lead.
“I feel like I'm doing a good job of getting the ball in position and giving myself a lot of looks," Scheffler said. “I feel like I burned a lot of edges the first couple days. Once those putts start falling a bit more, I think I'll start scoring a bit better.”
Carlos Ortiz of Mexico and defending champion Viktor Hovland of Norway each had 65 and were three shots behind. Hovland overcame a bizarre break on No. 1 after he made the turn when his approach took a wild bounce and went out-of-bounds, leading to double bogey.
“I pushed it a little bit and literally landed four steps right of the pin, hits a sprinkler head and goes in the trees over the green,” Hovland said. “That’s a bad break, but it’s not like I sliced it OB or something like that. I knew I was playing good golf, so I just had to reset.”
That he did, making five birdies the rest of the way.
It doesn't take much to get out of position, and the leading players all spoke of the importance of keeping the ball in play.
Brooks Koepka was doing the same until the worst moment. He rallied to get inside the cut line only to pull his drive into the mangroves left of the 16th. He took a penalty drop and his next shot stayed just short of more trouble. He made triple bogey, had another 71 and missed the cut. Koepka hasn't finished in the top 20 since July.
Rickie Fowler got his mistakes out of the way early. He played the par 5s on the front nine with a bogey and a double bogey, and then failed to birdie the par-5 13th. He was just outside the cut until a birdie on the 17th for a 72 to make it on the number.
The cut was at 4-under 138.
Ten players were in a tie for fifth at 9-under 135, a group that included Justin Thomas. The surprise in that group might be Bill Haas, who is using a one-time exemption for career money to keep a full card this year.
Haas, who won the FedEx Cup in 2011 and played on two Presidents Cup teams, has gone more than six years without a win and is No. 744 in the world. He opened with a 65 and had another bogey-free round of 67 to stay in the mix.
“I’ve been grinding for seems like three years now on trying to figure out what’s going to be consistent and what’s going to help me get over that hump,” Haas said. “Right now I have a swing thought that seems to be working OK. And I want one to last for more than two days. I'd love for it to continue this way and hopefully have a nice few months.”