Ameer Webb of Texas A&M won the race in 20.10 seconds with Mississippi's Isiah Young second in 20.17.
Nellum, who won the 400-meter final Saturday, finished the 200 in 20.27 seconds.
Brown, who was fifth in the 100-meter final on Saturday, finished the 200 in 20.33.
USC had entered Saturday tied with Texas for the men's team lead with 32 points.
But with several events remaining, Texas A&M had vaulted into first place with 51 points. USC was in second place with 42 and Oregon was third with 38.
USC's women's 400-meter relay team finished seventh. Texas A&M won the event in 42.88 seconds. The Trojans finished in 44.48.