Chappell finished the tournament at 2-under-par 286. The Pac-10 Player of the Year also led after Wednesday's first round and had a three-round total of 210 after shooting a third-round 68.
Indiana's Jorge Campillo and Washington's Nick Taylor tied for second, three shots back at 1-over.
Clemson's Kyle Stanley trailed Chappell by four strokes after Friday, but he shot 10-over-par 82 Saturday to fall from second into a tie for seventh. Stanley was the runner-up last year.
As expected, Augusta State missed the cut after finishing the third round Saturday morning. The Jaguars shot their best round of the event, 14-over-par 302, but finished 29th out of 30 teams at 72-over.
While the team was absent for the final round, freshman Henrik Norlander advanced in individual play.
Norlander's third round 73 had him tied for eighth going into the final 18 holes. But he struggled to 12-over-par 84, finishing tied for 29th.
UCLA finished the four-day tournament with a 42-over-par total of 1,194, one stroke better than second-place finisher and defending champion Stanford, which was five strokes back on Friday.
Southern California finished two strokes back at 1,196. Ten-time NCAA champion Oklahoma State and Clemson rounded out the top five.
Clemson was near the lead throughout the tournament and was tied for second coming into the final round, just three shots back of UCLA.
The Tigers shot 22-over-par 310, their worst round of the event by eight shots, for a fifth-place showing. Clemson finished the event at 49-over.
The top five teams were separated by just seven shots, the closest stroke margin for the top five teams at the national tournament since 2003, when Clemson won by two shots over Oklahoma State.
Georgia shot 21-over-par 309 in the final round to finish at 58-over.
The Bulldogs tied for eighth place with Charlotte, which shot a final-round 303.
The tournament was played on Purdue's 7,450-yard, par-72 Kampen Course and ended with the top 15 teams playing for the title. Friday's third round was suspended because of inclement weather and was completed early Saturday.