Nellum, a 2012 U.S. Olympian from Los Angeles, clocked a personal-best 44.73 seconds to finish ahead of Texas A&M's Deon Lendore (44.94 seconds) and Florida's Arman Hall (45.02).
Nellum's victory earned 10 points, giving USC 32. Texas is in second place with 31 points, Arkansas is third with 26.
Brown, a junior who competed for Canada in the 2012 London Games, on Friday finished fifth in the 100-meter final, clocking 10.01 seconds.
USC senior Reggie Wyatt won the 400-meter hurdles in 48.58 seconds.
Alitta Boyd and Melia Cox were competing Friday in the final of the women's triple jump.