Spaniard Jon Rahm, the beaten finalist last year, is another player making an early exit after failing to win for the second day in a row but Rory McIlroy bounced bounced back from an opening loss to beat Jhonattan Vegas of Venezuela 2&1.
The four times major champion could still win his group but needs to beat American Brian Harman on Friday.
World number four Jordan Spieth remained perfect with a 4&2 win over China's Li Haotong.
Johnson never led against Hadwin, who was surprised by his opponent's lacklustre form.
"I played extremely solid all day," Hadwin told Golf Channel. "I made the putts from five-to-seven feet when I needed to for par to keep the momentum on my side.
"I really expected Dustin to play a lot better than he did. I think everybody did coming in this week. Just a few putts he missed and here we are," he added.
"I kept putting the pressure on him. He needed to play well in order to come back."
Hadwin faces Wiesberger on Friday while Johnson plays Kevin Kisner, who still has a chance of topping the group and being among the 16 players to advance to the knockout phase.
Rahm, meanwhile, was beaten 1-up by American Chez Reavie, a result which sealed the Spaniard's fate following his halve with Keegan Bradley on Wednesday.
Thai Kiradech Aphibarnrat (2-0-0) leads the group after beating Bradley 1-up.
Spieth enjoyed his second straight win but is not assured of winning his group as Patrick Reed is also 2-0-0 after beating South African Charl Schwartzel 1-up.
Reed won in style when his ball struck the pin with his approach at the 18th, settling an inch away for a conceded birdie.
Spieth and Reed, team mates on the U.S. Ryder Cup and Presidents Cup squads, meet on Friday to determine who advances.
World number two Justin Thomas also scored a second straight win on Thursday, beating Patton Kizzire 3&1, and will meet Italian Francesco Molinari on Friday. The Italian has also won his opening two games.
(Reporting by Andrew Both in Cary, North Carolina, editing by Ed Osmond/Peter Rutherford)
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