Grabau was 4 of 5 from 3-point range and scored a career-high 20 points. Cooke was 6 of 7 on a variety of dunks and layups and also had a tip-in to notch his second career double-double with 12 points and 11 rebounds.
Jerron Granberry added 12 points for Wyoming (4-1), which led for all but 14 seconds and will visit No. 8 Ohio State on Monday.
Grabau drilled his first 3 and has made 61 percent of his long-range shots this season (14 of 23).
"I was feeling just like every other game, feeling good," he said. "My teammates trust me in taking that shot, so that takes a lot of pressure off me. They give me the ball in the right place and I just knock it down."
Cooke said he is trying to stay in his comfort zone by taking close shots.
"Coach says do what you do in practice like in the game," Cooke said. "He says take shots you usually make."
South Dakota (0-3) was led by Brandon Bos with 12 points and Tavian Pomlee with 10. Trevor Gruis had 10 rebounds and eight points. The Coyotes were only 25 percent from 3-point range (6 of 24) and 32 percent overall. For the season, the team is also hitting 25 percent from beyond the arc and coach Joey James said the early season shooting woes concern him "a little bit."
"But I tell you what: I've got enough confidence in our guys that those shots are going to start going in," he said. "Right now, they're rushing things a little bit. We're just inconsistent on the perimeter right now. We've gotta get better at it. Some of that had to do with Wyoming's length. Some of that had to do with our guys having to get a little more confidence."
The Cowboys shot 50 percent overall, including 53 percent from 3-point land (9 of 17). It was the third straight game of netting at least half their field goal tries.
"It starts with (Josh) Adams and Grabau out front," Wyoming coach Larry Shyatt said. "They made good decisions to start the game. They got us in a good flow. We had good ball movement on offense -- a lot of extra passes that got us some open looks."
Adams and Grabau had combined for an uncharacteristic 10 turnovers in the prior game. Friday they combined for two.
South Dakota trimmed a first-half 18-point deficit to seven after a putback by Gruis early in the second period. The Coyotes would draw no closer as the Cowboys stretched the lead to 50-37 after a 3-pointer by Granberry, then took their largest lead at 67-45 following a layup by Cooke with 2:29 to play.
Wyoming erased an early 4-3 deficit and exploded on a 17-1 burst over 4 1/2 minutes to go up 33-15 after Cooke's tip-in with 6:30 remaining in the first half. Charles Hankerson Jr. sank a 3 and hit two layups and Granberry added five points during the blitz. The Cowboys settled for a 40-27 lead at the break.