Reserve Allie Quigley scored 17 and Sylvia Fowles added 12 points and 12 rebounds for Chicago (13-16). Elena Delle Donne finished with 15 points.
The Sky moved into a tie for third in the Eastern Conference with the win and losses by the New York Liberty and Indiana Fever.
Rookie Alyssa Thomas had 15 points and six rebounds for the Sun (11-19). Kelsey Bone added 14 points and eight rebounds.
Connecticut rookie Chiney Ogwumike missed the game after having an abscessed tooth drained earlier Tuesday. She is the Sun's leading scorer and rebounder.
Prince scored 10 unanswered points late in the third quarter. That included three layups, two of which resulted in three-point plays, and helped Chicago to a 58-51 edge.
"I just wanted to be aggressive, and I felt like Sasha (Goodlett) and (Jessica) Breland were setting good screens in transition," Prince said. "I was trying to take advantage of the post player trying to stop me."
Chicago had trailed the entire third quarter until Prince's surge.
"We were disruptive," Sky coach Pokey Chatman said. "Alyssa Thomas had 12 points at half and finished with 15. (The Sun) were not challenged in the first half. (Thomas) was getting touches in her comfort zone. She was just having her way with us."
The Sky got off to a slow start offensively, but shot 63 percent in the second half.
"We married that defensive (third) quarter to some offensive execution," Chatman said. "The ball wasn't sticking as much. I thought early on we let the ball stick and didn't move it around as much."
Connecticut missed 21 of 23 shots in the third quarter.
"And Epiphanny just lit up at that point in time," Sun coach Anne Donovan said. "We had some breakdowns defensively in that quarter on her. We were trying to trap her off of every ball screen and we had some breakdowns from our posts on those traps, which led her into the paint."
Chicago missed eight of 12 shots in the first quarter, but led because it kept getting to the free-throw line. It made all 12 of its foul shots that period and led 20-19 after one.
Connecticut had just six free-throw attempts in the first half.
The Sun put together a 14-4 run to take a 37-32 lead with 2:17 left in the second. Bentley started the run with a 3-pointer, and Douglas capped the surge with another 3.
Connecticut led 41-36 at the break, but Prince took over in the third.
"Amazing," Chatman said. "She was snaking it and taking it to the basket and getting some and ones. But she was so good defensively, things that maybe a fan wouldn't see. She was so locked into the schemes and their actions and communicating that to others and that's what you like."