Spieth was 19 when he became the youngest player to win on the tour in 82 years at the John Deere Classic, a victory that helped propel him to No. 22 in the world rankings.
That win put him into this exclusive event and he took full advantage on a windy day at the Kapalua Resort by firing a 7-under 66. He was tied for the lead with Michael Thompson, Chris Kirk and Webb Simpson, with whom Spieth was paired for the first round.
The winds swept across the island of Maui from the north following overnight rains, the opposite direction from which the breezes usually blow at this event.
That did not deter the members of the 30-player field, only three of whom failed to break par.
Spieth was the only one of the co-leaders to escape making a bogey and his round was highlighted by four birdies in the final five holes.
Kirk birdied the last five and Thompson had four birdies in the closing five holes.
This tournament has traditionally opened the PGA Tour season, but six events have already been played as part of the new-look schedule.
Moore comes into 2014 as the season's leading money winner, followed by 2013 Tournament of Champions winner Dustin Johnson.
Johnson settled for a 3-under 70 that left him tied for 11th. Current Masters champion Adam Scott, playing with Johnson in the final group of the day, also had a 70.