John Jenkins scored 13 for the Americans, who improved to 4-1 in World Cup qualifying from the FIBA Americas region.
Jose Alvarado of the New Orleans Pelicans scored 20 for Puerto Rico (2-3), while Gian Clavell scored 17. Ismael Romero added 15 for Puerto Rico.
"It was just a matter of us having the respect for them and the physicality of FIBA basketball and just being prepared for that," Jackson said.
The U.S. closes first-round qualifying play Monday at Cuba. The Americans have already clinched a spot in the second round, as has Puerto Rico.
"We have a high-character group that came to work," U.S. coach Jim Boylen said. "And they were very prideful in everything they did. I'm really thankful for that."
Jordan Bell sent the U.S. into the half with a 42-37 lead by banking in a 3-pointer that just beat the buzzer, then had words for the Puerto Rico crowd as he left the floor for intermission.
That seemed to fire up the Americans, who came out flying in the third quarter.
Galloway hit back-to-back 3s for a nine-point lead early in the quarter, and then Jackson took over. He scored nine consecutive U.S. points, that run ending when Cook connected on a deep 3-pointer from the left wing with 2:49 left for a 63-46 lead.
Puerto Rico chipped away, but the Americans still carried a 15-point lead into the final quarter after another beat-the-clock score -- Eric Mika's tip-in as time expired in the third for a 66-51 edge.
The Americans kept the lead the rest of the way. Alvarado made a 3-pointer with 14 seconds left to get Puerto Rico within 81-75, but the outcome was already decided.
"Regardless of the outcome, this is a special moment in my life, for my family and the guys that have the jersey on with me," Alvarado said. "We're making memories, we're growing together and we've got a country on our side. We're going to represent as best as we can. I know we didn't win today but this is the beginning of a great start."
The records from the first round carry over to the second round, composed of six more games starting in August. Only Canada (5-0) and Brazil (5-0), who are playing in other first-round groups, have better records than the U.S.
The Americas Region will see 12 teams make the second round of qualifying, and of those, seven will play in the World Cup -- the main qualifier for the 2024 Paris Olympics.
CANADA 95, DOMINICAN REPUBLIC 75
At Hamilton, Ontario, Shai Gilgeous-Alexander scored 15 of his 32 points in the third quarter to lead Canada to an easy win.
Kelly Olynyk scored 17 points and hauled in 11 rebounds for Canada. Nickeil Alexander-Walker, who is Gilgeous-Alexander's cousin, also had 17 points.
Victor Liz scored 12 points for the Dominican Republic.
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