DURHAM, N.C. -- Duke didn't have to make a second-half escape plan Saturday.

The top-ranked Blue Devils took control early in a 96-80 victory against visiting South Dakota.

"I thought we got a lot out of the afternoon," Duke coach Mike Krzyzewski said. "I wish we had played better in the second half, but that's part of the development."

Grayson Allen scored 19 of his 25 points in the first half as Duke made a rousing return home at Cameron Indoor Stadium.

After a whirlwind opening three weeks of the schedule, the Blue Devils looked comfortable in their first home game since Nov. 20. They didn't have to sweat this one out despite a rather unimpressive second half with Krzyzewski opting for numerous substitutions.

"It wouldn't have been 56-30 at halftime (if we didn't play well)," Krzyzewski said. "I was trying to get playing time for the bench."

Marvin Bagley III poured in 19 points to go with 12 rebounds for the Blue Devils (10-0), who played a home game for the first time in five games. Bagley, a freshman forward, has double-doubles in eight games.

"It was good getting back to play on our home floor," Bagley said.

Trevon Duval's 14 points and Javin DeLaurier's 13 points also bolstered the Blue Devils, who've reached the 85-point mark in all except one game this season.

Duke, which became the country's first 10-game winner this season, trailed in the second half in each of its previous four games. This went much smoother from the outset with a crisp first half of offense.

"The hospitality has been incredible," South Dakota coach Craig Smith said, "except for the first 12 minutes."

It took the Blue Devils less than 17 minutes to build a 28-point lead.

Duke shot 62.2 percent from the field in the first half. The Blue Devils had twice as many rebounds (26-13) as South Dakota (7-3) by halftime.

Duke missed only 14 first-half shots, yet tracked down rebounds on nine of those.

In the second half, the Blue Devils committed 14 of their 19 turnovers.

"We understood that we were up by a lot and then we stopped playing hard," Duval said.

The Coyotes outscored Duke 50-40 in the second half.

"We didn't get any stops," Allen said, referring to the second half. "We have to get stops. We've got to be better on that end."

South Dakota forward Tyler Hagedorn and reserve forward Nick Fuller each scored 16 points. Matt Mooney, who scored 30 points in Thursday night's 82-63 victory at Missouri-Kansas City, was held to three points.

Allen provided much of the early defense on Mooney.

"(Duke) made it very, very difficult to get touches (for Mooney)," Smith said. "Mat showed some frustration that he doesn't usually show. They did a great job to make him work for everything."

The Coyotes had been off to their best start since winning their first 14 games in the 2007-08 season.

NOTES: Duke logged about 8,500 miles in November, but it will play four of its five December games at home. ... This was the first time South Dakota faced an Atlantic Coast Conference member, though it played Florida State and Notre Dame before those schools joined the ACC. ... This marked the first time Duke took on a team from the Summit League. ... Since becoming a Division I team, South Dakota is 0-6 against ranked opponents. ... Duke is home Tuesday night against Saint Francis (Pa.). ... South Dakota played its fifth consecutive game away from home. The Coyotes have a home game Wednesday against Drake.