Amile Jefferson had 17 points and 13 rebounds while freshman Frank Jackson finished with 11 points and keyed a timely 11-0 run for the Blue Devils (7-1).
They won their fourth straight despite shooting just 27 percent from 3-point range.
Eron Harris scored 14 points for Michigan State (4-4). Playing their first game as an unranked team since March 2015, the Spartans had 18 turnovers and star freshman Miles Bridges was held to 11 points — six fewer than his team-leading average — on 4-of-13 shooting.
Neither team led by more than four before the Blue Devils broke a 48-all tie by reeling off 11 straight points, a run that coincided with a series of Spartan slaps to the floor — one of Duke's trademark moves.
Seconds after Bridges gave the floor a firm slap, Jackson blew past the Michigan State guards for a layup that gave Duke its largest lead to that point, 55-48, with just under 13 minutes left.
Michigan State: Coach Tom Izzo has admitted he might have overscheduled these Spartans, whose four losses have all come to teams ranked 16th or better in the current AP Top 25, with the last two coming against top-10 teams. They've only played twice so far at the Breslin Center, but at least they won't have to leave East Lansing again until Dec. 27.
Duke: Allen was just 7 of 21 shooting in 37 minutes while playing three days after injuring a toe on his right foot during the Appalachian State win. The Blue Devils needed major minutes from him because they went just six deep — the five starters, plus Chase Jeter. Injured freshman forwards Harry Giles, Marques Bolden and Jayson Tatum once again took part in pregame warmups with varying stages of intensity.
Michigan State: The Spartans get some relief from their brutal early season schedule and begin a run of five manageable home games Saturday when they play host to Oral Roberts.
Duke: The Blue Devils wrap up their four-game homestand Saturday with a visit from Maine before returning to New York to face No. 24 Florida on Dec. 6.