And sixth-ranked Duke needed every bit of that production to hold off East Carolina.
Hood scored a career-high 30 points Tuesday night to help the Blue Devils beat the Pirates 83-74 in the NIT Season Tip-Off.
Parker had 21 points, nine rebounds and six blocks 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.
It was also the second game in as many nights for both teams, who were playing in a four-team pod at Duke's Cameron Indoor Stadium.
"The last two nights, we've played our butts off," Duke coach Mike Krzyzewski said. "This is not about Duke not playing [well]. ... Don't undersell what they did. We were ready and we played hard. I thought we brought great energy but so did they. This was a really good basketball game."
Duke led by a 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), earning a trip to next week's NIT semifinals in New York's Madison Square Garden.
Hood, a 6-foot-8 sophomore transfer from Mississippi State, finished 8-for-10 from the field and hit all 12 of his free throws while playing nearly the entire 40 minutes.
Parker made his biggest impact with a couple of key second-half plays, from taking a rebound all the way for a team-rousing dunk to blocking consecutive shots with his team protecting a 75-70 lead.
"We couldn't scout them like we normally do and we tried not to stay in the gym last night and watch them play because we had a quick turnaround," Hood said.
"But they're a great team. They've got a lot of talent, especially for a mid-major. They played hard. They wasn't scared of us."
The Blue Devils, who beat UNC Asheville 91-55 on Monday night, cooled off significantly after a hot start and shot 47 percent, failing to reach at least 50 percent for the first time this year.
The Pirates had a much tougher time in their Tip-Off opener, needing to rally from 17 down after halftime to beat Norfolk State 76-74. That game at Cameron marked a return to unfriendly surroundings for Pirates coach Jeff Lebo, who played for Dean Smith at hated rival North Carolina in the 1980s.
Lebo's team turned in a strong fight less than 24 hours later, but couldn't pull off a huge upset.
"We can draw a lot from this -- our kids playing in this stage, this environment," Lebo said. "We don't get a chance to do that too often. We draw a lot of positives, and when we watch the tape, I think we'll get some confidence from that.
"And then we've got to be able to build up on it. We can't say, 'Hey, we played well and we're done for the year.' "
Prince Williams scored 15 for the Pirates, who shot 40 percent and 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 an 11-for-11 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 from there.
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 after his coast-to-coast dunk, swatting a leaner from Williams out of bounds and then stuffing a driving shot from Antonio Robinson with about 2 minutes left.
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, who beat Florida Atlantic on Friday night, are off until Sunday, when they host Vermont.
"Now we've got to rest," Krzyzewski said. "I mean, our guys are dead."