Oscar Alvarez struggled to a round of 73 to finish one shot back at even-par 140. Alvarez, who held the first-round lead, was joined by Nick Cook in a tie for second.
Moore, who earned his second U.S. Amateur Public Links title earlier this year, started on the 10th tee of the West course on Tuesday and stumbled out of the gate with bogeys on each of his first three holes.
'You're going to make some bogeys out here,' said Moore. 'Sometimes, they'll come three in a row.'
The 21-year-old recovered with a birdie at the par-four 18th and moved up the leaderboard on the front side. Moore made it two in a row with a birdie at the first and added back-to-back birdies starting at the par-five fifth to reach two-under.
Moore, who won the NCAA individual title this year as a junior at UNLV, faltered with a bogey at the eighth but was able to finish alone on top. He will now move on to the first round of match play in an attempt to redeem himself from last year's championship when he was eliminated in the first day.
'It would be awesome to win here,' he said. 'Especially since I won the Public Links earlier this year.'
Alvarez collected five bogeys to go along with two birdies for his share of second.
'I didn't putt good,' said Alvarez. 'But, three-over par on this course is not bad.'
Cook mixed four birdies and three bogeys for a round of 69.
'The golf course is so tough,' said Cook. 'The greens are so severe on the West. You can't go hunting birdies. You can get yourself in trouble.'
Bronson La'Cassie took fourth place at one-over-par 141. Luke List, Chad Poling and Andy Svoboda followed at three-over-par 143.
A total of 77 players survived the cut, which fell at 10-over-par 150. There will be a playoff at 7:30 a.m. (et) Wednesday among the 18 players at plus-10 to reduce the field to 64 for the first round of match play.