World No.20 Leishman will be in the second last group and likes his chances of making up the four-shot deficit.
Major winners Rory McIlroy and Jason Day also ended the day tied for sixth alongside Kizzire.
Tway at least fared better than Johnson, who pulled his drive into a penalty area at the fourth and was then directed to his ball by a marshal.
Rory McIlroy watches his missed birdie putt on the 17th green during the first round of the Tournament of Champions golf event Thursday, Jan. 3, 2019, at Kapalua Plantation Course in Kapalua, Hawaii.
The US PGA Tour is trialling on-course interviews during play at its first event of the year and Leishman was one of the first to face the microphone during a windy opening round in Hawaii.
Thomas, however, said he would not be putting with the flag stick in.
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Johnson shot 24-under 268 a year ago to win by eight strokes.
"I'm certainly not blaming my bad shot on it".
"I'm comfortable on this golf course and I've enjoyed the last couple of days like flighting different shots, hitting different trajectories and with all the technical work I have had to do in the off-season, it is a real contrast to come out here and completely forget about the swing and just hit the shots", he said. "I was walking up to 16 green, so it wasn't as though it was right before".
"I've had a lot of thinking to do and I've come to the realisation that for me to base myself in the United States and play a bit more over here will be the best for me, my game and my career".
"If you get the wrong gust of wind, you can make a fool of yourself so to be able to get in at four under is a nice start to the tournament".
Johnson, the defending champion and two-time victor at Kapalua, has never shot over par in 32 rounds since coming here for the first time 10 years ago.
Once on the green, a three-putt resulted in a triple-bogey seven but he stormed home with a birdie on the ninth and five more on the back nine. "So just first time, I'm just focusing on that to be honest".
Marc Leishman on his way to a 68 at Kapalua today. "They weren't too happy that the ball went in, so it made me laugh", he said.