The American trio sit on six under, with Tway - making his tournament debut after claiming a maiden PGA Tour title in 2018 - firing seven birdies in a bogey-free 66 to grab the early advantage.
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Day is joined at four under by four-time major victor Rory McIlroy, Bryson DeChambeau and three others. In his favor is the history at Kapalua.
The former world No.1 started Friday just one shot off the lead.
"That's the only time I would pull the flag out". It's nice to build off those and take certain things out of them.
"I played well today, I drove it good", Johnson said. He showed his experience on the par-5 18th, when he missed the green to the right and faced an extremely fast putt with the grain and wind.
Marc Leishman looks for his ball out of bounds along the 17th fairway during the first round of the Tournament of Champions golf event, Thursday, Jan. 3, 2019, at Kapalua Plantation Course in Kapalua, Hawaii.
Leishman also signed for a 68 that left him well within reach in outright third place at 13 under. "That's been tough", Woodland said.
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Morata finally had the ball in the net after half time, slamming from close range after fine work on the right from Hudson-Odoi. Alvaro Morata scored the two goals but it was not quite the flawless send off for Fabregas, who missed from the penalty spot.
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McIlroy managed to get through it without a bogey. "I regrouped after missing a short one on nine, chipped in there (on 11) and got it rolling". He made his par to at least stay in range.
Woodland and fellow big bomber McIlroy will play in the final group. One of those was the Masters, the missing leg of the career Grand Slam, when he started two shots behind Patrick Reed and never challenged.
Maybe this ace will give him some more momentum. "I mean, I can deal with a little bit of dizziness for sure".
"Nah that was just me; that was just a shit shot", Leishman joked.
And Koepka will face stern competition from a field which consists only of PGA Tour winners from the previous calendar year.
Thomas, however, said he would not be putting with the flag stick in.
"I just saw somebody's face in the background". And while it's not like a lot of other players are going out getting hammered every night, golf has a more social reputation than most sports. Johnson and Thomas are the past two winners at Kapalua.
Gary Woodland was tied for second at 67 with Justin Thomas, the 2017 victor here who birdied five of the final seven holes, and defending champion Dustin Johnson.