CHICAGO -- Duke coach Mike Krzyzewski issued an important clarification to a crowded room of reporters as he praised the hot hand of senior shooting guard Grayson Allen.

"He's a great shooter," Krzyzewski said. "He's not a good shooter, he's a great shooter."

Few could argue the coach's point after No. 1 Duke pulled away for an 88-81 victory over No. 2 Michigan State on Tuesday night at the United Center.

Allen scored a career-high 37 points and hit several big shots in the final minutes to help Duke (3-0) remain unbeaten.

"I felt like I was hot from (3-point range)," said Allen, who made 11 of 20 shots from the field and 7 of 11 from beyond the arc. "For me, when I get a few open looks, the basket looks bigger."

Guard Trevon Duval (17 points, 10 assists) and forward Wendell Carter Jr. (12 points, 12 rebounds) each posted double-doubles for the Blue Devils. Duke beat Michigan State for the seventh time in a row.

Forward Jaren Jackson Jr., guard Miles Bridges and forward Nick Ward scored 19 points apiece in a losing effort.

Michigan State (1-1) was outrebounded 46-34 and allowed Duke to pull down 25 offensive boards.

"I'm embarrassed, to be honest with you," Michigan State coach Tom Izzo said. "Never in a million years did I think we'd get outrebounded like that. ... We deserved what we got. They deserved what they got."

Both teams made big shots during a back-and-forth game that included 11 ties and nine lead changes. After Michigan State forward Kenny Goins and Carter Jr. traded thunderous dunks to even the score at 75, Duke guard Gary Trent Jr. hit a 3-pointer to put the Blue Devils up 78-75 with 3:11 to go.

Allen followed with a 3-pointer to increase Duke's lead to six points with 2:27 remaining. The scoring binge reminded Krzyzewski of former Duke guard J.J. Redick, a sharpshooter who went on to earn millions in the NBA.

"You keep calling plays for him," Krzyzewski said. "I felt like I was coaching Redick. Grayson was fantastic."

Michigan State overcame a double-digit deficit early in the second half with a 12-2 run to even the score at 56. Ward punctuated the run with a layup and a free throw with 12:27 to play.

Duke built a 38-34 lead at the break. Allen beat the buzzer with a deep 3-pointer from the top of the key to cap an 8-0 run for the Blue Devils to close out the half.

The Spartans trailed by as many as 10 points in the first half before responding with an 11-0 run to seize a 25-24 lead. Jackson Jr. hit two 3-pointers during the run to spark the rally.

Izzo said he would review the game tape to determine how his team was outmuscled so badly in the paint.

"This is about building a team," Izzo said. "This is about getting better every day."

NOTES: Duke F Marvin Bagley III headed to the locker room after he was inadvertently poked in the eye by a teammate in the first half. Bagley returned to the bench to start the second half but did not play. Duke coach Mike Krzyzewski said Bagley scratched his eye but is not likely to miss much time. ... Michigan State F Ben Carter went down in the second half but remained in the game after he drew an elbow from Duke F Wendell Carter Jr. ... Duke G Grayson Allen scored in double figures for the third time in as many games this season. He has scored in double figures 67 times during his collegiate career.