Rodney Williams added 13 points and 11 rebounds for his first double-double of the season, and Trevor Mbakwe had 12 points for the Gophers (10-1), who led all the way on their first trip to play USC in Los Angeles since Dec. 29, 1980.
"This is a huge win for Coach's career," Hollins said. "Part of the history books. Obviously, it shows how great of a coach he is, how great a person he is and it is translating over to us being a winning basketball team."
Smith became the 19th active Division I coach to reach that win mark, something he didn't realize until being told.
"It was good to do with this group," he said. "There's always a challenge with any group, but this group is a committed group, they have great chemistry, so it's fun to coach them."
Reserve Omar Oraby scored all of his 15 points in the second half to lead USC (3-6).
Byron Wesley added 13 points and Jio Fontan had nine. DeWayne Dedmon grabbed 10 rebounds. The Trojans have lost five in a row and six of seven.
"We never put any real pressure on them at all," USC coach Kevin O'Neill said. "We got much better in the second half and played harder. These are the things we have to do to get better."
USC cut its deficit to single digits for the first time in the second half on a basket by Oraby with 5:41 remaining. He struggled at the line, making just 1 of 5 free throws. That was the closest the Trojans came as Hollins scored six of the Gophers' final 10 points.
"We were just kind of passing the ball around, not making them play defense on us. We didn't take advantage of that, that's how the game got close," Hollins said.
"We need to attack the gaps and make them play us. Instead we were playing outside of them, not being aggressive so that's one of the things we have to get better at as a team."
USC committed 17 turnovers, went 1 of 11 from 3-point range and got beat on the boards 40-32. The Gophers had 10 steals, although they had 15 miscues.
The Trojans improved their shooting to 45 percent in the second half, when they were outscored 33-31.
Oraby was involved in the game's hardest foul when he and Mbakwe both went down early in the second half. Mbakwe went to the line and made both free throws to extend the Gophers' lead to 49-36.
"We each hit pretty hard. I didn't think it was a foul," Oraby said. "I only blocked the ball. I didn't touch his arm."
The Gophers raced to a 23-10 lead, including the game's first nine points, before the slow-starting Trojans played them nearly evenly the rest of the first half. Fontan made 5 of 6 free throws as USC closed the half by outscoring the Gophers 16-15 to trail 38-26.