Cook scored 18 points, grabbed six rebounds and had three steals to lead the No. 17 Ducks to a 100-82 win over Dons on Sunday.
"Elgin really helped us," coach Dana Altman said of the redshirt sophomore transfer from Northwest Florida State. "He made some tough shots, was active on the boards. He was a real difference maker."
Senior Mike Moser also praised his teammates' aggressive play against the Dons.
"He's our X-factor," said Moser, who scored 13 points and had eight rebounds. "He just brings a whole 'nother dimension to our team."
The Ducks (4-0) had six players score in double figures, getting 17 from Damyean Dotson and 16 from Jason Calliste.
Kruize Pinkins had a game-high 20 points for San Francisco, but Oregon held the usually high-percentage shooting Dons (3-3) to 36.8 percent and 8 of 28 from 3-point range.
"At the end of the game, I wanted to attack the basket but we settled for 3s," Dons coach Rex Walters said. "We didn't seem to fully buy into that, and that's what it takes to play in these types of environments against a tough team like this. We were right there on the verge. We let it get away from us a little bit at the end."
Altman criticized his team's defensive effort after a 69-54 win last Tuesday against Utah Valley, and he said Sunday's play was better. Still, it's a long way from where he would like to be with a tough stretch of games upcoming.
"They're playing hard," Altman said, "and trying to get there, but we just have a tremendous amount of work to do."
Oregon's first three baskets were 3-pointers, but the Dons -- despite missing 10 straight shots -- took the lead on a layup from Cole Dickerson with 14 minutes left in the first half.
The teams traded baskets before Oregon started to pull away. Moser sparked a 10-3 run after taking a charge with 5:56 to go in the half. He scored on the other end on a 5-foot floater, then Dotson slashed to the hoop for two more points, giving Oregon a 32-24 lead.
Dotson gave Oregon a 10-point advantage at 37-27 on a dunk, and a 3-pointer from Jalil Abdul-Bassit pushed the Ducks' lead to 40-29 at the two-minute mark of the first half.
The Dons closed with back-to-back 3-pointers from Chris Adams to cut Oregon's lead at halftime to 40-35.
Dotson hadn't scored more than nine points in a game this season and had missed all nine of his 3-point attempts. Sunday, he hit his first 3-pointer with 16:06 left in the first half and he finished the game 7-for-12 shooting from the field.
"I wasn't focused (before)," Dotson said. "I was pressing. This game was different. I wasn't forcing anything."
Altman said the change from Dotson was noticeable.
"It was real nice to see him get a couple shots down," he said. "It improved his energy."
Oregon weathered a run by San Francisco that cut the score to 44-41 early in the second half. The Ducks responded with an 8-2 run, capped by a 3-point play from Calliste that brought the lead to 59-46 with 14 minutes left in the game.
The Dons rallied to 61-55 midway through the second half, but Oregon hit 3-pointers on consecutive possessions to go back up 12 with 9:25 to go, and San Francisco didn't threaten the lead again.
The Ducks led by as many as 19 in the second half and shot 32 for 60 from the field and 58.1 percent from 3-point range.
Sunday's attendance at Matthew Knight Arena was 6,084. ... Oregon's six players in double figures was its most since an exhibition game against Division III Willamette in 2010.