Freshman Jabari Parker had 21 points and nine rebounds for the Blue Devils (4-1), who survived a tougher-than-expected fight from the underdog Pirates to improve to 24-2 all-time in the early season tournament.
Duke led by a single point with about 7 minutes left but stayed in front and did enough in the final 2½ minutes to turn away East Carolina (4-1).
The Blue Devils advanced to next week's semifinals in New York's Madison Square Garden.
Prince Williams scored 15 for the Pirates, who shot 40 percent but helped themselves by hitting the offensive glass for a 16-3 edge in second-chance points. East Carolina fell to 0-21 all-time against Duke, though the Pirates flirted with earning their first win against a ranked opponent in nearly 11 years.
Duke led by 18 points late in the first half after a hot-shooting start, but the Pirates didn't let the Blue Devils put together a knockout run. Instead, the Pirates closed the gap to 11 by halftime, and then kept inching closer and closer after halftime.
East Carolina twice got within a point, the last coming on Williams' free throws with 6:58 left, but never could push in front.
Duke helped itself by playing with composure down the stretch, hitting all eight of its free throws in the final 2:34 to stay in control. Parker also came through with a big defensive sequence with Duke protecting a 75-70 lead, swatting a leaner from Williams out of bounds and then stuffing a driving shot from Antonio Robinson.
Hood hit two free throws to make it 77-70, and East Carolina didn't get closer than five again.
Duke finished 24 for 31 from the foul line, including 19 for 24 after halftime.
The Blue Devils beat UNC Asheville 91-55 on Monday night, getting 21 points and 10 rebounds from Parker while Hood finished with 18. The Blue Devils shot 57 percent in that one, the fourth straight time they had shot better than 50 percent to open Mike Krzyzewski's 34th season in Durham.
The Pirates had a much tougher time in their Tipoff opener, needing to rally from 17 down to beat Norfolk State 76-74. That game at Cameron Indoor Stadium marked a return to unfriendly surroundings for Pirates coach Jeff Lebo, who played for Dean Smith at hated rival North Carolina in the 1980s.
When Duke couldn't miss to start the game, it looked as if Lebo's Pirates were in for a miserable night.
The Blue Devils hit their first 11 shots and didn't miss until nearly 9 minutes into the game, with Parker's dunk and Hood's driving basket giving them a 23-9 lead in that opening flurry.