Scheffler was 5 Up after 11 holes against Johnson and looked to be making serene progress into the final for a second consecutive year at Austin Country Club.
But the former World Number One won four holes in a row from the 12th to trim the gap to one before Scheffler took the 16th and 17th to advance.
Victory in the final will see Scheffler replace Jon Rahm at the top of the Official World Golf Ranking but he will first have to get past a man who won this event in 2019 after losing in the final the year before.
Scottie Scheffler vs. Kevin Kisner— WGC-Dell Technologies Match Play (@DellMatchPlay) March 27, 2022
Winner takes all. pic.twitter.com/yNck5tdyVO
A favourite among the local crowds due to his days at the University of Texas, Scheffler has proved himself to be an excellent match play operator, getting all the way to the final here last season and then winning 2½ points in the United States' record Ryder Cup victory.
He has two wins from six starts in 2022 but has not had it all his own way this week, needing a play-off to get out of Group Five and being taken to the last by defending champion Billy Horschel in the last-16.
But he will head into the final full of confidence after coming through an almighty battle with Johnson.
Scheffler put an approach to seven feet to birdie the first and left himself just four feet at the third as he quickly moved 2 Up.
Johnson three-putted the fourth and failed to get up and down after missing the green at the next but was given hope as a ragged tee-shot from Scheffler saw him lose his first hole of the day at the ninth as the gap was cut to three.
SCOTTIE 😱— PGA TOUR (@PGATOUR) March 27, 2022
Almost an albatross from 250 yards out. pic.twitter.com/CnNBzJhQ19
But Scheffler put his second on the tenth to tap-in range and then got up and down on the 11th after missing the green, a trick that Johnson could not repeat as the lead went to five holes.
Sand off the tee at the 12th meant Scheffler was forced to lay up at the par-five as Johnson made his birdie, and he lost another hole after finding water off the tee at the 13th.
All of a sudden, Johnson had his tail up, and he played a sensational approach to 11 feet at the 14th and bombed a drive to leave himself a simple wedge into the next to make it four in a row and cut the advantage to one.
But Scheffler was inches from an albatross on the 16th, making his birdie as Johnson missed a short putt to match, and the two-time Major Champion shook hands on the next with his opponent left with two putts from eight feet for a half.
Kisner has now won 22 of his 29 matches played at Austin Country Club since 2016 and showed all his battling qualities against Conners in a match where nobody was more than 1 Up until the handshakes.
"It felt like a heavyweight bout," he said. "He's a hell of a ball-striker, always in play, hitting great shots after great shots. Fortunate enough to come out on the right side of this one for sure.
"Scheffler is on a heater. Obviously I need his putter to cool off for me to have a chance. But I want to keep staying annoying out there and see what happens."
Kisner holed a 20-footer to birdie the second but Conners responded from half that range on the next before a 14-foot birdie from Kisner on the seventh put him ahead at the turn.
Conners needed an incredible up-and-down from the left of the green to halve the tenth and that seemed to provide him with fresh impetus as holed a 40-footer for birdie on the next and went 1 Up as Kisner found water on the 12th.
A poor second and chip from Conners handed Kisner the 14th and the 38-year-old won the 17th with par after getting up and down, claiming the last as he used the contours around the green to put a beautiful second to four feet.