Only the top five teams in the 14-team field will qualify for the NCAA Championships and Auburn is in seventh place after Thursday's competition.
Auburn's 288 total is even par and 11 strokes off the pace of 277 set by Texas A&M and TCU. North Florida is third at 280 followed by Texas Tech at 282, Wichita State at 283 and Pepperdine at 286 at The Traditions Club.
Moreland shot a round of 69, which is three strokes off the pace and tied for sixth. He made the turn at five-under-par after making an ace with a six iron at the 216-yard ninth hole.
He holed out his approach shot to the green on the par five 584-yard fifth hole for another eagle. However, on the back nine he had four bogeys to go with two birdies and three pars.
"I got to five-under pretty fast," said Moreland, who noted he had one previous hole-in-one, but not in a tournament. "I knew it went in. I had to hit a hard six to get over the bunker and landed it right where I had hoped it would, and it rolled down and happened to hit the hole and go in."
Sophomore John Stembridge shot a 71, sophomore Will McCurdy finished at 72 and freshman David Zickler was the other scorer at Auburn with a 76. The Tigers didn't have to count an 80 posted by sophomore Kyle Kopsick.
Auburn coach Nick Clinard said the Tigers need to pick up their level of play on Friday. "We played pretty well overall," he said. "We struggled out of the gate and played really well in the middle of the round. We went from five-over to five-under and then struggled the last two holes in which we could have played better.
"This is the first NCAA regional for all five of our guys as a team," he said. "They may have had a little bit of nerves at the start, settled in during the middle and started to think about their score at the end. That is typical with younger players doing that instead of just letting it happen."