It all added up to another win for No. 23 Connecticut and new coach Kevin Ollie.
Napier scored 10 points during a 12-0 run that put the Huskies ahead for good midway through the second half. UConn (3-0) took a 65-55 lead on DeAndre Daniels' driving layup with 6:18 remaining.
Wake Forest (1-1) pulled to 73-69 on Travis McKie's 3-pointer with 53 seconds left, but Napier knocked down four free throws over the final 28 seconds to clinch it for UConn.
"Shabazz finally showed up for us those last (10) minutes," said Ollie, who replaced retired Huskies coach Jim Calhoun this season. "I'm glad he did."
Wolf and Daniels each added 12 points for the Huskies, while Wolf, a 7-foot-1 junior, had six rebounds.
"Enosch was huge," Ollie said. "He did a wonderful job. It seemed like we had a big presence, a big fella down there. That felt good, coming down the stretch. He wanted the ball down the post. I liked his confidence."
Wolf played 25 minutes, nearly doubling his previous career high of 13, thanks largely to foul trouble incurred by starting forward Tyler Olander.
"I've worked hard for this; I got a chance," said Wolf. "I've got to show what I can do and keep going from here."
In a back-and-forth affair that saw eight lead changes and two ties, UConn made five of its final six shots in the first half to take a 36-32 lead into halftime. Daniels had 10 points at the break.
Wake Forest went on a 10-0 run, highlighted by consecutive 3-pointers from McKie and Arnaud William Adala Moto, to take a 50-46 lead with 12:08 left.
Napier hit a driving layup to bring the Huskies within one, then Wolf's 17-foot jumper from the wing put UConn ahead for good, 53-52.
"It was a great game, a hard-fought victory," Ollie said. "We stayed within our game plan. Defensively, I thought we made the key stops when we needed them. That's something we pride ourselves on."
Boatright, a 6-foot guard, led UConn with seven rebounds.
The Huskies shot just 3 of 18 from 3-point range but made 80 percent (24 of 30) of their free throws. Wake Forest went just 55 percent (12 of 22) from the foul line and turned the ball over 18 times.
McKie grabbed eight rebounds for the Demon Deacons and Devin Thomas had seven.
"Basketball's a game of runs," McKie said. "The first half was kind of evenly matched. The second half we came out and attacked. They had a late run, and we never recovered from that. They're a very good team. We have several freshmen, it's a great game for us to build on. We have another game tomorrow."
UConn, which won the Paradise Jam in its last appearance at the event in 2008, will now face Quinnipiac on Sunday night. Wake Forest will face Iona on Saturday.