Doughty made it 2-0 at 15:10 on a one-timer from the left circle during a power play.
Pacioretty cut it to 2-1 at 7:24 of the second period when Reilly Smith's shot from a sharp angle redirected in off his skate. The play was looked at to determine if Pacioretty used a distinct kicking motion on the goal, but the call stood after a video review.
"Any time the confidence is down, it seems like every chance against ends up in the back of your net, but we got to fight through it," Pacioretty said.
Prokhorkin, who was playing his fifth NHL game, scored to make it 3-1 at 9:08 of the second at the left post after Kyle Clifford couldn't control the puck in the slot.
"First goal's special, so you could see it on his face," Clifford said. "Obviously, he's been working pretty hard the last five games and it's good to see."