Another pair of Aggies in the race included Kevin Burnett, who placed fifth in 14:05.88, while MacLean O'Donnell finished seventh in a career best 14:14.09, which is sixth best on the A&M all-time list.
In running his first 5,000 meters of the season, Lelei lowered his previous best of 14:13.75 as he ran a series of 65-second laps at the end of the race before producing a 59-second lap to pull away for the victory.
"It was very good for my first outdoor 5K on the NCAA level," Lelei said. "13:50 is good to start out with. I was just trying to maintain a good pace. I wanted to get around 13:45, but it was hard to get at that pace early in the race. The last four laps were good, so it was a good start.
"It was a very nice night to race. It was like back home, everything was perfect with a cool evening. It was very pleasurable for a distance run."
Lelei is the second best performer with the second-fastest performance on the Aggie all-time list, moving ahead of a pair of Barrios performance marks, a 13:51.10 also in Austin from 1985 and a 13:55.16 by Barrios at the Southwest Conference meet in Fayetteville.
Four years after setting A&M school records, Barrios ran a career best of 13:07.79 in the 5,000 meters and also set a world record of 27:08.23 in the 10,000 meters in 1989 and held it for four years.