"When you get up real early, you just want to keep the momentum on your side," said Johnson.
Rory McIlroy and Jordan Spieth were surprise losers in their first round-robin matches at Austin Country Club.
McIlroy, who reached last year's semi-finals, fell 2&1 to Dane Soren Kjeldsen while Japan's Hideto Tanihara, making his first appearance at the tournament, routed Spieth 4&2.
Kjeldsen was 1-down with five to play but rattled off four successive birdies, knocking his last four approaches inside nine feet, with the last three inside four feet.
"I played well. If I had played anyone else, I might have won. Soren played great," said McIlroy.
Northern Irishman McIlroy will play Gary Woodland on Thursday and Argentine Emiliano Grillo on Friday. Woodland beat Grillo 3&2.
Twice major champion Spieth never led against Tanihara, who has 13 career titles overseas. The American played his last nine holes in three over, hitting only one green.
"I knew if I brought my 'A' game, I could probably compete against him," said Tanihara. "I wanted to see how a top player would play and I was just looking forward the whole day."
Next up for the Texan is a clash with Japan's Yuta Ikeda on Thursday and Ryan Moore on Friday. Moore halved his match with Ikeda.
Japan's Hideki Matsuyama and U.S. Ryder Cup Captain Jim Furyk halved, while Brooks Koepka was lights out with the putter in a 6&5 trouncing of fellow American Kevin Kisner.
Day, last year's winner, walked off the course after six holes, revealing to reporters that he was leaving to be with his mother, who is having lung cancer surgery on Friday.
"Hard to comprehend being on the golf course right now with what she's going through," said a tearful Day. "Family is first."
The event is comprised of 16 four-player groups who play round-robin matches from Wednesday through Friday with the winners of each group advancing to a single-elimination bracket at the weekend.
Players receive one point for a win and a half-point for a halved match.
(Reporting by Larry Fine in New York; Editing by Frank Pingue)
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